solve the equation

[half rune]

equation

[half rune]

nah bro

it is have a solution

[restive kettle]

what do you solve for even

[half rune]

x

[restive kettle]

okay

didn’t know if it was like a simplification or anything

[half rune]

okay

[half rune]

okay

[restive kettle]

x = ~1.72?

[half rune]

yes

but I want the exact value of x

[frigid star]

!status

[opaque ether]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[half rune]

I mean the steps

[half rune]

2

[frigid star]

What do you have so far?

[waxen bane]

well cube root -1 = -1

[half rune]

I found this after some simplifications

[half rune]

how

[waxen bane]

-1 * -1 * -1 = -1

[half rune]

yes

[waxen bane]

i think thats gotta be one of the steps

[restive kettle]

x= ~1.71979673

[half rune]

i don't think so

[waxen bane]

so sqrt 3

[half rune]

the steps

[waxen bane]

lemme get some paper

[half rune]

okay

[restive kettle]

that’s the only answer i can get to so i yield

[half rune]

yes but I want steps

[restive kettle]

ahhh okay

[half rune]

because I have an exam ahah

[restive kettle]

gimme like 2 Mins

[frigid star]

I have a solution but it's probably not one you would like

[half rune]

tell me

[frigid star]

You basically already need to know the cubic formula

[waxen bane]

bruh

[half rune]

I think i know it

[frigid star]

$x$ is basically the descriminant of the cubic polynomial $t^3+pt+q=0$

[waxen pond]

SWR

[waxen bane]

damn

didnt even know it had a discrimnant

as in the discrimant like b^2-4ac?

[frigid star]

This equation describes $2$ as being a solution to the cubic with $x$ as the descriminant and with $-\frac q2=1$

[waxen pond]

SWR

[frigid star]

Descriminant of a cubic polynomial is slightly more complex

[half rune]

I think this solution is so hard hahah\

I want solution with rules of nroot cube

[frigid star]

For the depressed cubic $t^3+pt+q$, the descriminant is $\frac{q^2}4+\frac{p^3}{27}$

[waxen pond]

SWR

[half rune]

okay

[frigid star]

We have $q=-2$ and $t=2$ from here

[waxen pond]

SWR

[frigid star]

So you can solve for $p$ using this polynomial

[waxen pond]

SWR

[frigid star]

After having $p$ and $q$, you can finally get $x$.

[waxen pond]

SWR

[half rune]

bro sorry but i don't understand u

[frigid star]

Easy peasy

[frigid star]

I told you you wouldn't like my solution

[waxen bane]

well you could also see that left cubic of the left side must be an integer

and the right cubic must also be an integer

[half rune]

it is over my level hah

[waxen bane]

so the insides of the left cubic must be 27 and the other one 1

and then you can solve simulatneously

since 3 - 1 = 2

or keep trying values idk

[frigid star]

My solution actually doesn't work because this is a difference of cube roots. Oops

[half rune]

Yeah

[frigid star]

Cube both sides

[half rune]

already

I found this

[frigid star]

Cool. Put the cube root on one side and everything else on the other

[half rune]

okay

[half rune]

I found this

[frigid star]

how

[half rune]

hmmm

ahah

I sqrt(x)^2

(4+cbrt(1-x))^3

[frigid star]

I said to put the cube root on its own side

[half rune]

hmm

okay wait haha

nah wait

@frigid star like this

[frigid star]

Yes like that

now cube both sides

[half rune]

okay

[frigid star]

Looks good

[half rune]

yes

[frigid star]

make the replacement $y=\sqrt{x}$ and you are left with a non-trivial cubic polynomial

[waxen pond]

SWR

[half rune]

okay

what aboout

x = y^2 ?

$x=y^2$

[waxen pond]

! Mokatil Dev 💻⛏

[half rune]

I found $-y^3-15y^2-48y+91=0$

[waxen pond]

! Mokatil Dev 💻⛏

[frigid star]

yup

And then gg

[half rune]

now we should fin y hh

how

[frigid star]

It's non-trivial

You basically need the cubic formula

[half rune]

okay

math is hard bro

I spent 4h in my life hahah

[frigid star]

btw where did you get this problem from?

Because x is going to have a very non-trivial answer

[half rune]

I am study

in morocco

it is last year in high school

[frigid star]

Were you taught the cubic formula?

[half rune]

nah

[half rune]

we just learn cube root

[frigid star]

How does it want you to solve these? I doubt these want algebraic solutions

[half rune]

idk bro

I am just a simple student ahha

[frigid star]

You were given no solution methods?

There are several ways to work on each problem

[half rune]

nah

[frigid star]

graphing, estimation, calculation, algebraic

[half rune]

I will ask some teachers

[frigid star]

E3 and E4 are relatively simple

[half rune]

okay

[frigid star]

E1 is somewhat doable with creativity, but the answer is so ugly because of the fifth root of 2

But E2 straight up requires cubic formula, which most high schoolers are never taught

So that tells me that you were not meant to solve these algebraically, but perhaps through estimation with graphing

[half rune]

nah I mean algebraically

but I can't find it

[half rune]

you can help mee with E1

[frigid star]

E1 is the same approach as E2, but it won't end in a non-trivial cubic equation

Perhaps E2 had a typo..

[half rune]

okay

what's about E3

haha

[frigid star]

isolate the cube-root and then cube both sides

[half rune]

okay

thanks man for your heelp

How can I close this ?

.close