proof

[half hinge]

I just don’t get how you do proofs it’s so hard, can someone walk me through it please 🙁

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[steady bay]

So you want to do some algebraic manipulation so that you reach a recognisable equation that is correct

For example x^2>=0

So for this question square everything

Then expand (x+y)^2

And gather all the terms to one side

Then you'll end up with an expression that you could factorise

And the inequality must make sense

For example if you end up with (x+y)^2<0

Then you made a mistake somewhere

You must end up with a valid expression so that you prove that the equation from the beginning was valid as well

[uncut hinge]

How can you factorise if your going to have a x^2 and y^2

[steady bay]

x^2 +2xy+y^2=(x+y)^2

[uncut hinge]

Do you not get something like that?

[steady bay]

Yea

[uncut hinge]

Then how do you factorise

[steady bay]

After this you'll get x^2–2xy+y^2>0

[steady bay]

Same factorisation

But just negative y

(x–y)^2

[half hinge]

huh where did this come from?

I’m so confused 😭😭

[half hinge]

What do you do after this bit

[steady bay]

It's a factorisation

Try expanding it

[steady bay]

It'll give you that

[half hinge]

yeah but it’s +2xy so shouldn’t it be (x+y)^2 not (x-y)^2?

[gleaming berry]

u have to do it the other way around

u need to start with something that is true and then get to the statement in the question

[half hinge]

ok so what do I start with?

[steady bay]

No I subtracted the 4xy

[steady bay]

That's harder tho

[half hinge]

ohhhhhh

[gleaming berry]

start with (x-y)^2 >= 0 and then rearrange it to get the thing in question

[gleaming berry]

but its correct

the other way is wrong

[half hinge]

oh

the mark scheme is so confusing I don’t understand ir

[steady bay]

How come

[gleaming berry]

for example i could say

1 = 2

multiply both sides by 0

0 = 0 is true so therefore 1 = 2 is true

which is obvs wrong

[half hinge]

where did that come from?

[gleaming berry]

pattern recognition

(actually ive seen this question at least 10 times)

[steady bay]

I didn't say multiply by 0 tho

[half hinge]

huh so you just always start with (x-y)^2? I don’t get it 😔😔

[steady bay]

I did that in my final exams and got the whole marks for the question

[gleaming berry]

my point is you can't start with a statment, manipulate it algabraically and then get something true and conclude that implies the original statement

[half hinge]

??

and would you expand it out next

[gleaming berry]

yep

[half hinge]

okay then what

[gleaming berry]

actually for this question its easier to start with (root(x) - root(y))^2 >= 0

[half hinge]

😭😭

[gleaming berry]

ye but u can't do that

like if u do any maths at a higher level then that's completely wrong

[half hinge]

but where did you get the (x-y)^2 from (for future questions cuz I don’t understand any type of proof)

[steady bay]

What's wrong with that

[gleaming berry]

and the real examiners wont give makrs for that

[gleaming berry]

i told u why

u can't start with a statement, manipulate it algebraically, get something true and condclude the original statement was true

its just not how maths works

[half hinge]

idk how to do this 😭

[steady bay]

Im just working backwards like with trig proof questions

[gleaming berry]

u can't do that either

[half hinge]

@gleaming berry how do you know when to use (x-y)^2 pleaseee, do you just always use it 😭

[gleaming berry]

no

depends on the question

[half hinge]

how do you know that you have to use it now

[gleaming berry]

with proof there's no one thing u can do everywhere

[gleaming berry]

u kinda just look at it and think what might be useful

[steady bay]

What if it's a complex one

How do you know where to start

[gleaming berry]

what i would do is i would work backwards in rough to get an idea of what to do but when actually writing the answer i would go forwards

cuz that means ur actually answering the question thats being asked