# Homework Help: Quick question: x^2-y^2=16 (find x)

1. Feb 22, 2017

### sobergeek23

1. The problem statement, all variables and given/known data
x^2-y^2=16
isolate the variable x

2. Relevant equations
square roots

3. The attempt at a solution
x^2=y^2+16

x=y+4?

2. Feb 22, 2017

### BvU

Because your $x^2 = (y+4)^2 \ne y^2+16$

3. Feb 22, 2017

### sobergeek23

so whats the answer

4. Feb 22, 2017

### sobergeek23

if i squared both sides it would just be the individual answer

5. Feb 22, 2017

### BvU

What's the full problem statement ? 'Isolate' doesn't sound like a question with an answer ...

6. Feb 22, 2017

### sobergeek23

that was the problem..it just said isolate the variable x..

7. Feb 22, 2017

### Mastermind01

NO! This is a fundamental mistake. $\sqrt{a+b} \neq \sqrt{a} +\sqrt{b}$

8. Feb 22, 2017

### Mastermind01

Isolate probably means solve for x in terms of y.

9. Feb 22, 2017

### sobergeek23

said something like it is understood to be positive or something like that

10. Feb 22, 2017

### sobergeek23

we were solving equations where you square both sides

11. Feb 22, 2017

### BvU

In that case you are done when you write $x^2 = y^2 + 16$ : it has x in isolation on the left hand side of the $=$ sign.

12. Feb 22, 2017

### sobergeek23

it cant be a square

13. Feb 22, 2017

### Mastermind01

• Poster has been reminded (too late) not to post answers to schoolwork questions on the PF
So the answer is just $x = \sqrt{y^2 + 16}$ NOT $y+4$

14. Feb 22, 2017

### BvU

Rapid fire of posts from three sides ...

Ok, semantics: isolate means write it so that it says $x =$

What do you have to keep in mind when going from $x^2 = ...$ to $x = ...$ ?

15. Feb 22, 2017

### sobergeek23

why doesnt that reduce?

16. Feb 22, 2017

### BvU

Watch out MM ! PF hates direct answers. it ruins the learning experience

17. Feb 22, 2017

### sobergeek23

learning experience means frustration and anger and deletion of account for me...

18. Feb 22, 2017

### Mastermind01

Let's keep it cool. What's $(a+b)^2$?

19. Feb 22, 2017

### sobergeek23

a^2+b^2

20. Feb 22, 2017

### BvU

It does reduce, but you have to be careful...
I recognise the frustration and anger. Don't get carried away, sit back and think a bit now and then before firing of another post and the 'deletion of account' may be replaced by 'satisfaction from deeper udnerstanding'

21. Feb 22, 2017

### Mastermind01

NO. Let's multiply it out. $(a+b)(a+b)$ Do you know the distributive law of multiplication?

22. Feb 22, 2017

### G10rgos

• Newbie poster has been reminded (too late) not to give answers to homework problems here on the PF.
Let's take it step by step.
First things first, x2 + y2 is NOT equal to (x+y)2
That is because if we expand the second to (x+y)*(x+y) it's x*x + x*y + y*x + y*y which is equal to x2+2*x*y+y2.
This is the basic calculus formula for quadratic equations, which are equations to the power of 2.
Now, x2 + y2 is not the same as (x+y)2, using the rule above.
With another rule, we can expand x2 - y2 into this: (x-y)*(x+y), and to prove this we do the same as (x+y)*(x+y).
So: (x-y)*(x+y) is: x*x + x*y -y*x - y2 (plus times minus equals minus).
Therefore: x2 - y2.
So, going forward to your question,
x2 - y2 = 16 is as follows:
x2 = 16 + y2
x = √(16 + y2)

I hope I was able to shed some light for you.

23. Feb 22, 2017

### BvU

Hello G10,

That has come by already and was chastized as giving a direct answer (and a wrong one to boot). Please be a bit more careful next time.

24. Feb 22, 2017

### sobergeek23

yea i got it..is it because the plus sign is in there?

Last edited by a moderator: Feb 22, 2017
25. Feb 22, 2017

### sobergeek23

is it aginst forum policy to give out answers?