formula for this?

[gleaming gale]

Doesn't seem like there's an obvious (workable) pattern, so I would suggest solving for x in terms of a, then substituting in the second formula.

[woeful scroll]

ohh ok

[gleaming gale]

!nosols

[nimble kayak]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[subtle geode]

my bad

[gleaming gale]

It's alright.

I do like the method

[subtle geode]

but yes exactly this, there isnt a clear relationship between the two you kind of have to play around with the equations

[woeful scroll]

yeahh hpw do solve for x

[subtle geode]

im not sure you need to, i think it just wants an expression for the second equation in terms of a

[woeful scroll]

huh so wdid

[subtle geode]

if you mean how to find an equation for x in terms of a, like Fern mentioned you want to find a way to substitute the first equation into the second (solve for x in terms of a), e.g

finding the square of both a and x, and using that
or
finding the reciprocal of both sides of the first equation and using that

etc.

[woeful scroll]

is it this

[gleaming gale]

$x^4+3x^2+1$ is distinctly not equal to $(x^2+3x+1)^2$

[mossy fjord]

A miscellaneous Fern

[gleaming gale]

I would suggest taking $x = a(x^2+3x+1)$, rewriting it as a quadratic equation, and solving for x

[mossy fjord]

A miscellaneous Fern

[woeful scroll]

question, whats a quadratic equation again

idt ive learn that yet

[gleaming gale]

$AX^2+BX+C = 0$

[mossy fjord]

A miscellaneous Fern

[woeful scroll]

huhhh unfamiliar

what

wait

whys there c

and b

[gleaming gale]

Oh really

Huh.

Well in that case you can still take the equality x = a(x^2+3x+1) and get some work done with it.

@subtle geode Had good ideas for manipulations

[woeful scroll]

is my everything at left side correct?

[gleaming gale]

Yes, the left side is fine

[woeful scroll]

is it possible to make x^2 from left side equal to x^4+3x^2+1

idkkk how manipulations can help w it

like

i cant see any other form

[glass glen]

i suggest you learn it

[woeful scroll]

self learn? ehhh i need notes then

[upper raft]

just divide the numerator and the denominator by x and in the second equation by x square, after that you will see that x+3+1/x =1/a and by raising it to the send power you will get the the second equation’s denominator.

[woeful scroll]

then
first equation:
x+3+1/x = 1/a

wait what

do i power the 1/a ?

PLEASE TELL ME IM RIGHT

[upper raft]

almost right but it will be 6 not 3 then since (a+b) square is a square + b square +2ab and this 2ab part becomes 6 since 2•3•x•1/x is 6. now let’s say the second equation equals b. Thus 1/b = x2+3+1/x2 if we divide numerator and denominator by x2 .

[woeful scroll]

this 6 u mean?

what

oh

yeah

[upper raft]

yeah

[woeful scroll]

lets just say ik the (a+b)^2 formula but i dont rly understand the concept im just memorizing it lol

[jade tapir]

you dont understand the binomial formular? 😔

[upper raft]

you can’t remember(a+b)^2 formula? u just need to practice with it a lot.

[woeful scroll]

no i mean

i remember it

but i dont know the concept

like im just memorizing it dumbly

so thats why idk how to apply formula in questions

[woeful scroll]

whatever that is... i call it algebra formula

[upper raft]

I know the best way to understand it intuitively.

[woeful scroll]

please

[upper raft]

i

[woeful scroll]

oh wow

let me process and look

[upper raft]

that’s the way I learned it

[woeful scroll]

i feel like its more complicated

like

[upper raft]

lol yeah that’s might be complicated if you are not good at geometry.

[woeful scroll]

if i do it in algebra way, (a+b)^2 = (a+b)(a+b) right

which is

a^2b+ab^2

isnt it

[upper raft]

yeah that’s a good way to understand it

[upper raft]

how did you get that?

[woeful scroll]

like how can it become a^2 + 2ab +b^2

[woeful scroll]

cuz like

a(a+b) = a^2b

then the second part

b(a+b) = ab^2

and add

together

= that

[upper raft]

(a+b)(a+b)=a(a+b)+b(a+b)=a2+ab+b2+ab

[upper raft]

that’s not correct

[woeful scroll]

OH

YES

I FORGOT MY ALGEBRA WORKS LIKE THAT WITH THOSE COMPLICATED SHIT

[upper raft]

4(a+b)=4a+4b isn’t it?

[woeful scroll]

YES YES

[upper raft]

😂

so you struggle with when to use this formula right?

[woeful scroll]

yeah

not just that

every formula

like if its not direct idk what formula to use

[upper raft]

you just need to do a lot of practice , just find a book with similar similar problems and do them daily. It’s the only way to understand it.

[woeful scroll]

i have a lot alot alot more questions like this

that idek how to do

[upper raft]

I guided you a way to solve your question. Try another approach and decide which one is more suitable for you.

[woeful scroll]

wait wheres the (a+b)^2 thing in this question

[upper raft]

aren’t they about the same topic?

[woeful scroll]

kinda but theres even more formulas

like its a topic where we learn a bunch of formulas

and questions whereu might need to mix formulas

but once again i dont understand the formulas and is just memorizing them

[upper raft]

you don’t need to understand the formulas. You can prove them based on easy steps. However you don’t need it now. You just need to learn how to apply them correctly. Just memorize them for now. Focus in the problems

[woeful scroll]

but some of the questions r too random like i dont see the formula

this for example and the formulas i learnt are

[upper raft]

then ask me and I will guide you or your teacher

[upper raft]

oh that seems funny!!! let’s say that this expression is equals to x then multiply both sides by (2-1)

[woeful scroll]

why 2-1

[upper raft]

because (2-1)(2+1)=(2^2-1)
then (2^2-1)(2^2+1)=(2^4-1)
and so on until we reach the last one

[woeful scroll]

sooo keep doing it?

[upper raft]

basically our goal is make from large expression a smaller one. and the best way to do that is applying (a-b)(a+b)=a2-b2 !!!

[upper raft]

yep… and after few times you will understand how it will end

[woeful scroll]

wait let me attempt doing it in the dumb way first

[upper raft]

every time you just get (2 in the twice bigger power -1)

[upper raft]

waste of time. but You can do that if you want

[woeful scroll]

wait but it's supposed to be 2^2+1 not -1

[woeful scroll]

ah then nvm

[woeful scroll]

but once again i dont see the formula

wheres a and where b

[upper raft]

why? isn’t the formula (a+b)(a-b)=a2-b2??? not a2+b2

I agree those questions aren’t for beginners in this topic.

[woeful scroll]

year8

[woeful scroll]

oh so the -1

isnt referring to the question

cuz the question is (2^2+1)

but the formula shows -1 right

OH

NVM

I GET IT

-1^2 = +1

right

[upper raft]

THANK gods

[upper raft]

yeah

[upper raft]

[woeful scroll]

wait so this

[upper raft]

yes?

[woeful scroll]

but how can i multiply the long ahh expression by (2-1)

dont i have to do it one by one then

cuz idk whats in between

i mean i know

[upper raft]

you don’t need to write the whole equation, we’re looking at one part of it.

[woeful scroll]

right so i only multiply the part i can see with (2-1)

[upper raft]

the first part (2-1)(2+1) become (2^2-1) then we multiply it with other guy next to him and so on… just try it few times and you will get it

[upper raft]

yes

[woeful scroll]

ehh okay wait il ltry first

use this (2^2-1) to multiply w other or

(2-1) to multiply

[upper raft]

(2-1) has dissapeared already with 2+1

[woeful scroll]

disappear? liek this?

OHHH

its

(2^2+1)(2^4+1)

this

[woeful scroll]

or that

[upper raft]

2-1 * 2+1=2^2-1

[woeful scroll]

yeah

but isnt it

-1^2

cuz the formula

need to power it as well

[woeful scroll]

huh

[upper raft]

it's not -1 it's 1

[woeful scroll]

waitttt

[woeful scroll]

yeah

[upper raft]

is that clear to you? 100%?

[woeful scroll]

wait wat

wait

[upper raft]

it's not -1!!!! you should raise 1 to the power of two and then add - there

[woeful scroll]

yk im taught that the term comes with the minus symbol is that true

thats messing with my mind rn

but doesnt the minus symbol always come with the term b (aka 1)

so -b / -1 same thing

then -1^2 = 1

[upper raft]

NOOO!!!

minus doesn't has anything to do with b

[woeful scroll]

oh wadafak my teacher always teach the symbol b4 the term is like togther

[upper raft]

I think you just misunderstood her or sth....I hope the part with why (x-1)(x+1)=x^2 - 1 is clear

😭 pls

[woeful scroll]

shouldnt there be a ^2 at the -1 (or 1) tho

cuz following the formula

a^2-b^2

[upper raft]

lemme make it clear it's :( (a^2)-(b^2) ) minus seperated from b^2!!!

[woeful scroll]

OKAY OKAY SO THE 1 DONT HAVE ^2 BECAUSE 1 X 1 = 1?

[upper raft]

it's not a^2 (-b^2) no!!!

[upper raft]

yESSS you can write 1^2 if you want but 1 in any power(rational) is always 1!!!

[woeful scroll]

okay okay i understan

[upper raft]

yaaay

[woeful scroll]

ill just have to ignore what my teacher said about the -b and -1 shit

[upper raft]

yes just forgot it!!!

for god sake

since you understood this part look at this

[woeful scroll]

oh wait i kept thinking its ^6, ^8, ^10 after the ^4

like the ...

[upper raft]

their power sequence is 2^0,2^1,2^2,2^3,2^4......2^10

the powers of two

[woeful scroll]

huh the last one is 2^2^10 which is 2^1024 (i used calculate to cheat ;-;)

the power sequence is add 2?

or multiply 2

[upper raft]

multiply

[woeful scroll]

and i need another tutorial on how you find that out but that will be for another time cuz im exploding

[woeful scroll]

wait yeah i understand the part

but how can i find it out

in a simpler way instead of doing it one by one until i get 1024

[upper raft]

other ways we won't be able to solve this question....there're only 10 expressions

[glass glen]

that is (a-b)²

[woeful scroll]

huh

[woeful scroll]

so the only way is doing it one by one

[upper raft]

oh yeah now I understood what she meant.....however let's talk about after solving this question.

[glass glen]

idk whats happening xd

[upper raft]

I also barely understand, they gave her olimpic questions after just teaching binomial expressions.

[glass glen]

🤣

[upper raft]

I think so.

[woeful scroll]

ahhh okay but even after doing it

[glass glen]

@woeful scroll can you repost the original question?

[woeful scroll]

i stil have to somehow like power everything and find the answer?

like solve 2^2+1, 2^4+1, 2^2^10+1

[glass glen]

wait thats different than the first one

[woeful scroll]

that one is solved kinda yeah

im exploring the formulas

[upper raft]

noo you just need to multiply it by (2-1)

noting is going to change since (2-1) is 1 and if you multiply anything by 1 nothing changes.

[woeful scroll]

like (2-1)(2^4+1) = (2^4+1)?

but that wont give the answer of what 2^4+1 is

[upper raft]

noononono, look at my solution

I multiply (2-1) and (2+1) first

they become (2^2-1)

[woeful scroll]

yeah i understand all that but at last u still have to find what 2^2^11 is right

[upper raft]

then I multiply (2^2-1) with (2^2+1)

[upper raft]

well it's 2^2048 and I think it's enough

the goal was simplify the expression ig . In the test you will have a)2^2^11,b)2^1024 etc...

[woeful scroll]

ehhh i guess but honestly i wouldnt have seen the expression as a2-b2

[woeful scroll]

i hope cuz its

[upper raft]

now you know how to solve this kinda of questions

[woeful scroll]

not multiple choice

[woeful scroll]

yeahhh

i ust have to

observe better

[glass glen]

so 2^2^10 its equal to 2^1024 right

[upper raft]

if you just write 2^2^11 everthing will be ok.

[woeful scroll]

yep

[woeful scroll]

okok

now ill go do other questions

tysm

(watch me ask for help again in the forum in the next sec)

[upper raft]

alright, just ping me

[woeful scroll]

honestly, how is a2-b2 (a-b)(a+b)
like the (a+b)^2 thing i can understand easily bcz its bracketed then only the power

but that

how do i separate it to understand it in a similar way as a+b)^2

[upper raft]

sry for handwriting

[woeful scroll]

hm i think i got it

[upper raft]

great!!

[upper raft]

write down it by yourself as well to understand it more efficiently

[woeful scroll]

hold on a sec so green( what i always do) is wrong
cuz i never knew u can do like red( what u did), so meaning its possible to separate the a+b when multiplying?

OH

I DID THE GREEN WNOGLY

[glass glen]

search up multiplication properties

[woeful scroll]

so its the same

[glass glen]

one is:
(a+b)c = ac+bc

you cant remove the () on a+b like that

[woeful scroll]

ah yes i just messed up cuz i messed up

wait what

so green is correct

and red is ??

[glass glen]

its the whole (a+b) multiplied by the whole (a-b)

[woeful scroll]

erhhh

so red is

correct or wrong

[glass glen]

correct

[woeful scroll]

AHH I GET IT

[glass glen]

green wrong red correct

[woeful scroll]

this green?

old green i did mistake

[glass glen]

green is wrong when you go to the 2nd step

[woeful scroll]

new green i checked again

[glass glen]

yes

[woeful scroll]

so new green = red

[glass glen]

this one is wrong on the 2nd step

[upper raft]

red one is correct

[woeful scroll]

huhhhhhh

[woeful scroll]

red one is urs lol

green one is what i always do

[upper raft]

yeah, so what can't you understand?

[upper raft]

so don't do it!!!!

[glass glen]

the green mistake is you did
(a+b)(a-b) = a + b(a-b)

[woeful scroll]

like how did u just separate out the (a+b) to multiply w (a-b), thats possible?

[woeful scroll]

isnt that the same thing

its like

the purpose of the bracket

[glass glen]

no different

[woeful scroll]

is to signal multiplication

oh

what

ive been doing math for 14 years and knowing it today

[glass glen]

the same as b(a-b) + a

[woeful scroll]

like expanding right

[upper raft]

always do multiplications this way.

[woeful scroll]

hmm wait

[glass glen]

if you lose the brakets you are just multiplying the b now

and before you were multiplying the whole (a+b)

like
3+2(1+1) is different from (3+2)(1+1)

[woeful scroll]

oh so its like
3+2x(1+1) and (3+2) x (1+1)

[upper raft]

just put real number in the formula first calculate it without the formula then apply the formula and you will understand how does it work

[glass glen]

yeah, when we use brackets we usually dont add the x sign

so (a+b)x(a-b) = (a+b)(a-b)

[woeful scroll]

its not important to understand how it works right

[glass glen]

it is :)

[woeful scroll]

oh

i guess now i understand

[glass glen]

that * is multiplying, but we usually dont write it if there is brackets

like when we say ab its a*b

idk if there is any more doubts

[woeful scroll]

wait do i do (a^2-b^2) + (a^2-b^2) + (a^2-b^2) to find a^6-b^6

so its like 3 (a+b)(a-b)

[upper raft]

noooo it will be just 3(a^2-b^2)

[glass glen]

i dont think so

[woeful scroll]

which is 3(a+b)(a-b)

the formula

right

[upper raft]

before making such a statement put numbers to prove it. for instance let's take a=2 b=1 so you're saying 3(2^2-1)=2^6-1 which is 9=63 which is not true!!!

[glass glen]

the first sum isnt equal to 3(a+b)(a-b)

[woeful scroll]

ohh erhh

[glass glen]

whats the problem you are solving?

[woeful scroll]

this

im trying to see if i can actually adapt to the questions w the formula

and guess like i cant

how did the ^2 expanded version beceom the ^3 expanded version

[upper raft]

just rewrite a^6 as (a^3)^2

[woeful scroll]

OOH YES

this is what i mean when i say i cant put formulas in questions

cuz im not observant

[glass glen]

yeah thats exponents properties

[woeful scroll]

wait so (a^3)^2 - (b^3)^2 = a^6-b^6 is ((a-b)(a^2+ab+b^2))^2

[woeful scroll]

ah yes that ik

[glass glen]

its just really hard to see with all of these symbols xd

[woeful scroll]

true true

[woeful scroll]

wait is this correct

[glass glen]

write that and send a pic

like in a paper

[woeful scroll]

a board

[upper raft]

replace a^3 with x and b^3 with y

it will become x^2-y^2

[glass glen]

you really mean ab^2 or (ab)^2

[woeful scroll]

(a^3)^2 - (b^3)^2 = a^6-b^6 is ((a-b)(a^2+ab+b^2))^2

this ab?

[glass glen]

now thats different than the pic 🫠

[woeful scroll]

oh what

[upper raft]

yes a^3-b^3 becomes (x-y) and a^6-b^6 becomes x^2-y^2

[woeful scroll]

so im replacing an unknown term with another unknown term

ahhhhhh i feel like thats overcomplicating the original question which is to simplify

[upper raft]

yeah and in the future you will do it a lot,

[upper raft]

we're doing this to make you see which formular to apply

there's no formula for a^6-b^6

so that wee need to use a^2-b^2 formula

[woeful scroll]

oh wtf thats what ive been trying to find

cuz i thought u can make a^3-b^3 somehow that

ugh ill solve this tmr its so late alrd

my brain needs a night to process this x.x

wait theres a formula for a^3-b^3 right

[glass glen]

yea

[upper raft]

yeah but's harder to implement, better use a^2-b^2

[glass glen]

no stress, you will understand it all

[woeful scroll]

Wait if I use (a^2)^3

[upper raft]

use (a^3)^2 instead

[woeful scroll]

But it's harder to implement isn't it

a^3 = (a-b)(a^2+ab+b^2)

Ehh I'll go zzz and hope I dream about it so I won't forget

[upper raft]

yeah better go sleep

[glass glen]

id do this for the first division

actually put a plus sign at the end 🫠

[woeful scroll]

I figure it out, turns out the question is a bit wrong, the second part is (a^2-ab+b^2)

(a^6-b^6)/(a^3-b3) = (a^3)^2 - (b^3^2)/(a^3-b^3) = (a^3-b^3)(a^3+b^3)/(a^3-b^3)
Then cancel the same one and = (a^3+b^3)/(a^2-ab+b^2)= (a+b)(a^2-ab+b^2)/(a^2-ab+b^2)
And cancel the same one again = (a+b)

[woeful scroll]

also

i remember someone up there mentioned sth about simultaneous equation thing

is that related to algebra?

like the thing im doing rn

cuz i got this

and i thin its simultaneous equation

rn im trying to do al the questions by myeslf but it seems impossible

if its simultaenous equation, some1 please teach me

[upper raft]

hi, I have no idea what simultaneous equation is however I can tell you that (a+b)^2 and (a-b)^2 formulas are kinda similar but the difference is 2ab part. Just substract one from another and you will find that (a+b)^2 equals to.

[woeful scroll]

yeah i try that but it wont tell me what x and y each value right

wait

nvm

can i do like this

i feel like i cant

cuz itll make it to (x^2+y^2)(2xy)

stuck

oh wtf i did a mistake

(x-y)^2 does not equal to 8^2

stuck again

ando nce again im stuck

[subtle geode]

for the second line on the right, I believe you meant to write (x-y)^2 - also be careful when it comes to isolating your terms, to get rid of the 2(15) on the left side which is positive, you need to subtract 30 - opposite operations

also id recommend trying to let y(y+8)= -15, cos then you will definitely get a solution or two for y, so you can find what x is

[upper raft]

Jesus what’s that? let’s say that (x+y)^2=p we need to find p then right? So let’s find what does p-(x-y)^2 equals to, (x+y)^2-(x-y)^2=x^2+2xy+y^2-(x^2-2xy+y^2)=4xy
Thus p-(x-y)^2=4xy and p=(x-y)^2+4xy so we know the values of xy and (x-y) all it takes now just replaces them with their values

[woeful scroll]

ahh i get it now

so the goal is to

expand it so that u get xy and x-y then subsitute in the value

is it

ill try the other question:D

[woeful scroll]

PLEASE TELL ME IM CORRECT??

[woeful scroll]

i realize what i did wrong so this is the corrected (i guess) version?

AHHHHHHH IS IT CORRECT?

706

tell me im correct

im feelin gsmarter by each minute

how does this formula works? whats with the . . . in the middle

im tryna solve this

to feel smarter

[woeful scroll]

another one

[upper raft]

you’re still confusing the formula of a^2-b^2 however I’m glad seeing your progress. Here since you said x^4+y^4=p and we don’t have any formula for a^2+b^2 we can turn it into (a+b)^2 formula and we just need to add 2x^2*y^2. so p+2(xy)^2=(x^2+y^2)^2 and x^2+y^2 might be found through the formula a^2+b^2=(a-b)^2+2ab which were given to us.

[woeful scroll]

huuh which part of a^2-b^2 did i got it wrong

[woeful scroll]

ahh got it the mistake i did is (x^2)^2 + (y^2)^2 is not equal to (x^2-y^2)(x^2+y^2)

[upper raft]

yes!!!

your should try another approach

[woeful scroll]

erhh okay let me try again

[upper raft]

okay

[woeful scroll]

1156

or maybe 1606..?

[upper raft]

lemme check

I got 706

[woeful scroll]

oh what

[upper raft]

((x-y)^2+2xy)^2-2(xy)^2=(64-30)^2-2*15^2

[upper raft]

bro, x^4+y^4 is NOT (x^2+y^2)^2

[woeful scroll]

huh dont the power multiply w the 2?

[upper raft]

to make it easier to understand let’s say that x^2=a and y^2=b them x^4 will become a^2 and y^4 become b^2 do you agree with that?

[woeful scroll]

agree

[upper raft]

okay so we need to find a^2+b^2 right?

[woeful scroll]

yeah

[upper raft]

since we don’t have any formula for a^2+b^2 we need to find where it hides. For instance in the formula of (a+b)^2 which equals to a^2+b^2 +2ab. there a^2+b^2 = (a+b)^2 -2ab does that make sense to you?

[woeful scroll]

wait why -2ab not +2ab?

OHH

WAIT

I GOT IT

[upper raft]

great!!!

is everything clear so far?

[woeful scroll]

yes

[upper raft]

now let’s replace with the original values x^4+y^4 = (x^2+y^2)^2-2(xy)^2 is that clear?

[woeful scroll]

so the formula but with extra ^2

[woeful scroll]

this formula

[upper raft]

👍 yes

we just replaced a with x^2 and b with y^2

[woeful scroll]

ah so thats why at last its 1156-450

[upper raft]

since xy is given so we can say
x^4+y^4 = (x^2+y^2)^2-450

[woeful scroll]

cuz i did (x^2+y^2)+2(xy)^2 due to my wong undertanding

[upper raft]

no problem

we will work with that

[woeful scroll]

wait so techincally we can create formulas for like a^2+b^2 which doesnt have a formula?

[upper raft]

basically yes, but whatever we are doing is just simple algebra from (a+b)^2 formula

that’s why we don’t memorize it

[woeful scroll]

oh shi so theres even harder one x.x

wait dyk what this is

whats with the . . . in between

and the thetas thing

[upper raft]

did you understand the solution of previous one?

[woeful scroll]

yup

[upper raft]

you won’t need formula

[woeful scroll]

oh huh

theres a qusetion thats like x^5+y^5

[upper raft]

I had never seen a problem which needs this formula so far

[upper raft]

oh…

[woeful scroll]

yeah that

but im gonna ignroe the given ________ part

[upper raft]

I would just find the values of x and y if I were you

[woeful scroll]

oh okk

[upper raft]

just replace x=5/2-y and solve quadratic equation

[woeful scroll]

but sth weird is that (5/2) ^ 2 is not 13/4

[upper raft]

yes because you’re still assuming that (x+y)^2 is x^2+y^2

but it’s NOT!!!

[woeful scroll]

oh so ill just use the (a^2+b^2) = (a+b)^2 - 2ab formula

[upper raft]

(x+y)^2 is (x+y)(x+y) and x^2+y^2 is x•x+y•y!!!!

[upper raft]

you will just find what xy is but we need x it self so you need to replace y with 5/2-x and solve the quadratic equation

[woeful scroll]

erhh okay holdon

what's a quadratic equation..?

ik it's similar to sth ystrdy

except for that nothing else

[woeful scroll]

like this question

i find that x^2 = 25/4 - 25+y^2 and y^2 = x^2 = 25 - 25/4, ignoring quadratic equation cuz idk what that is

[upper raft]

wait you don't know how to solve the equations like x^2-5x+3=0?

[woeful scroll]

idk

like

my teacher said we haveto self learn it

cuz its not covered in the syllabus

means she expect us to know

[upper raft]

just look it up and you will understand how to solve that question below.

or ask chatgpt what quadratic equation is

[woeful scroll]

oh theres another formula for it .-.

[upper raft]

because idk how explain it

[upper raft]

yeah lol

the entire math is memorizing the formulas and performing them

[woeful scroll]

i feel like if ik the concept it should be fine?

must it always be ( ) + ( ) + ( ) = 0

or can the = not be 0

[upper raft]

even if it's not 0 we can substract it from both sides and get ( ) + ( ) + ( ) = 0

[woeful scroll]

ah i think i get it, so ill jst have to memorize the formula and im goodto go?

wiat hold on ima put this quadractic equation thing on hold cuz i just realize i havet finish another hw due tmr .-.

ah nvm im done

[upper raft]

yeah just memorize it,its proof is so complicated and even some university students don't know about it

[woeful scroll]

so proof is not important

[upper raft]

yes

our goal is just understand where to implement those formulas

[woeful scroll]

wait but whats with the + - thing on the square root

[upper raft]

yeah that means there're 2 solutions for this equation.

[woeful scroll]

ohh one negative and positive

[upper raft]

but rare one of them isn't true , and you have to decide which is our real x

but in this case both of them ok.

[woeful scroll]

wait so x = 5/2 - y

the 5/2 - y is the entire quadratic formula

ik te formula but idrk how it works, chat gpt said theres a,b,c but wheres my abc

x, y, 5/2 ?

what the shi

[woeful scroll]

do i haveto do this?

[upper raft]

x+y=5/2 isn't a quadratic equation by it self, you should replace y=5/2-x and then apply it on the second equation. like : x^2+(5/2-x)^2=13/2 then use (a+b)^2 formula to ease it

and you will get ax^2+bx+c=0

[woeful scroll]

(a+b)^2 or (a-b)^2 ?

[upper raft]

oh yeah (a-b)^2😂

you got me

[woeful scroll]

x^4 - 25/4(x) = 1 /4

[woeful scroll]

ah yess it feels like a st udent finding a mistake in the professor's working c:<

[upper raft]

yeah😂

[upper raft]

wait there no supposed to be x^4

[woeful scroll]

dont tell me i confused the formula again

ignore the arrow x^4 thing

[upper raft]

formula is okay but why 2*5/2x has become 25/4x???

2*5/2 is 5 isn't it?

[woeful scroll]

oh yah

5x right

sooo x^4 - 5x - 1/4 = 0

move the thing

[upper raft]

and x^2+x^2=2x^2 not x^4!!!!

[woeful scroll]

to make = 0

huh

[upper raft]

5+5=2*5=10 not 5^2 which is 25!!!

[woeful scroll]

oh x.x i confused it with the add power thing

[upper raft]

that's fine just don't it again

[woeful scroll]

so my a = 2x^2

b = -5x

c = - 1/4

[upper raft]

almost right but omit x

[woeful scroll]

oh what we can just cancel of the x?

[upper raft]

a,b and c are coefficients

[woeful scroll]

ohh

take the coefficients only

[upper raft]

yes

[woeful scroll]

wait so does the ^2 for 2x^2 comes along

[upper raft]

no!!

it's 2*(x^2)

[woeful scroll]

oh

x^2 is the term

[upper raft]

coefficient*(x^2)

[upper raft]

yess

[woeful scroll]

x = -5 + - square root 5^2 - 4(2)(1/4) / 4

[upper raft]

+5*

[woeful scroll]

isnt b = -5x = -5 tho

[upper raft]

the formula is -b+...../2*a

since b=-5 then -b is 5

[woeful scroll]

oh i get it -(-5) then - and - become +5

[upper raft]

yeah

we get a really bad number

so.....we should have tried another method

[woeful scroll]

huuuuuuuuuuuh

not another formula t.t

[upper raft]

don't worry there's no formulas just applying previous ones

let's say x^5+y^5 is p

and we can get x^5 by x^2*x^3 that's why we multiply (x^2+y^2) with x^3+y^3

[woeful scroll]

ah yes

[upper raft]

now all it makes just finding xy and x^3+y^3 which is more easier

[woeful scroll]

wait wiat why after x^5 + x^2 * y^3 + y^2 * x^3 + y*5 is p + x^2 * y^2 (x+y)

[upper raft]

we can find x^3+y^3 by this formula

[woeful scroll]

so x^5 + x^2 * y^3 + y^2 * x^3 + y5 is (x^3 + y^3)

[woeful scroll]

ehh what im confused wiat let me process

[upper raft]

I just rewrite the same thing in another order

[woeful scroll]

let me test it out wait

[upper raft]

okay no worries

[woeful scroll]

so this is also p + x(x^2y^2) + y(x^2y^2)

how is that 5x+5y tho

[upper raft]

it was just an example to show why it ends up outsite of the parentheses

[woeful scroll]

ohh

[upper raft]

so you get this part?

[woeful scroll]

the bottom is the up one expanded version?

wait but when i do x^2y^2(x+y) i get x^3y^2 + y^3x^2

[upper raft]

yes!!!

[woeful scroll]

huh what bout this

[upper raft]

I just substracted that x^2y^2(x+y) from both sides to find p

[woeful scroll]

huh- wasn't there only one side this whole time

[upper raft]

(x^2+y^2)(x^3+y^3)=p+x^2y^2(x+y)

[woeful scroll]

ohh this thing

[upper raft]

(x^2+y^2)(x^3+y^3) our initial expression

p+x^2y^2(x+y) final

[woeful scroll]

(x^2+y^2)(x^3+y^3) is the left side

ahh i got it

[upper raft]

yaay!! finally!!! so we can begin finding the values of (x^3+y^3) and xy

[woeful scroll]

(x^3 + y^3) = uhhh

create a new formula

liek the

(x^2 + y^2) right

[upper raft]

yeah I've wrote it before, we got it from (x+y)^3 formula

[woeful scroll]

huh

i jst realize i havent memorize the (x+y)^3 formula o-O

[upper raft]

here\

[upper raft]

fix it now!!!1

[woeful scroll]

ohh yes

(x+y)^3 = x^3 + y^3 + 3xy(x+y) ?

[upper raft]

if I were you I would memorize it this way:

[upper raft]

yess

[woeful scroll]

hm idk but i feel like ill be able to somehow get it by multiplying (x+y) 3 times

so shouldnt be a big worry

but just slower

[upper raft]

yes you can but why?

memorizing easier.

[woeful scroll]

my memory is too small for all the maths formula

that im pretty sure there will be even more forthe future

and other subjects stuff

[upper raft]

yes it's.....

[woeful scroll]

soo i rather save it for sth that actually requires memory like the quadractic formula

for now ofc

[upper raft]

but don't worry after some practice you will remember them all

[woeful scroll]

i hope

[upper raft]

you don't need it rn, since your teacher didn't teach you about it.

[woeful scroll]

well we r kinda expected to know it so

[upper raft]

you will see (x+y)^3 a lot!!! even in 11th grade

[upper raft]

if she didn't tell about it then not. You can learn if you want

[woeful scroll]

That's still a long period of time

But I guess

[upper raft]

I'm so tired, just try to find x^3+y^3 and xy and ask chatgpt if something. If even chatgpt won't help then dm me.

[woeful scroll]

Okok, go rest

(I have to sleep as well ._.)

[upper raft]

poor kid

[woeful scroll]

Oh wow

[woeful scroll]

-65/16?

I found xy = 1.5

[upper raft]

Hi again, it supposed to be -1/8

just raise (x+y) to the second power and you will see why.

[woeful scroll]

Ohh ok I'll try

Wait xy is -1/8 or the final answer

[upper raft]

xy

[woeful scroll]

Huh I did (x+y)^2 = (5/2)^2

Then (x^2+y^2+2xy) = 25/4

And since x^2+y^2 = 13/4, it'll be 2xy=25/4-13/4

[jade tapir]

yo where is the task? 😭

[woeful scroll]

Ahh

It's fine x^5+y^5 given (x+y)=5/2 and (x^2+y^2) = 13/4

[woeful scroll]

12/4 = 3 = 2xy

Xy = 3/2

[jade tapir]

ya seems right

[woeful scroll]

Either I'm wrong or I saw the question wrongly cuz I trust it's -1/8, it's prob another formula he was talking abt

I'm still testing ou the -1/8 tho

[upper raft]

wait wasn’t x^2+y^2 =13/2?

[woeful scroll]

Uhhhh wait I'll check

Nope it's 13/4

[upper raft]

you’re right then ,my bad

[woeful scroll]

Oh oh oh

[upper raft]

I’m too old to remember everything

👴

[woeful scroll]

Oh lol. If I'm considered young at the age of 14 then u??

I substituted everything and it's -65/16

[upper raft]

yep you’re a kid

[woeful scroll]

14 kid t.t

[upper raft]

I trust your answer. Too lazy to check

[woeful scroll]

Ah yes

[upper raft]

did you find x^3+y^3?

[jade tapir]

wasup unc

[woeful scroll]

Uhh

Yws

I used the expanded formula

[upper raft]

sup kiddo how is it going?

[woeful scroll]

And substitute in the value

[upper raft]

good

[jade tapir]

going good gang wbu

[upper raft]

not bad, just took my medication for my back.

[jade tapir]

shiiii

tf you do bro 😭

[woeful scroll]

Postgraduate... How old is that

Ehh whatever I'll consider myself graduated from the binomial expression thimg

Thank you for your help guys

[jade tapir]

uhh idk like above 23

[woeful scroll]

Oh that's not that old

[jade tapir]

says the 14 yrs old

[woeful scroll]

Just a 10 yrs gap..?

[jade tapir]

lmfao

[upper raft]

I’m only 18

[upper raft]

https://tenor.com/view/congratulations-gif-15313310096117360512

[jade tapir]

k blud

[woeful scroll]

Oh yeah and If u r old I should be consider as medium:D

Wait but postgraduate at 18???

Postgraduate of high school or uni

[upper raft]

I have no idea what it is.

Just randomly picked

[woeful scroll]

Oh cool I'm pre uni

My randomly picked role

[upper raft]

👍