Solving x² - y² = 16 for x

[sobergeek23]

Homework Statement

x^2-y^2=16
isolate the variable x

Homework Equations

square roots

The Attempt at a Solution

x^2=y^2+16

x=y+4?

 

[BvU]

Quick answer: No.
Because your $x^2 = (y+4)^2 \ne y^2+16$

 

[sobergeek23]

so what's the answer

 

[sobergeek23]

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

 

[BvU]

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

 

[sobergeek23]

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

 

[Mastermind01]

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

 

[Mastermind01]

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

Isolate probably means solve for x in terms of y.

 

[sobergeek23]

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

 

[sobergeek23]

we were solving equations where you square both sides

 

[BvU]

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

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.

 

[sobergeek23]

it can't be a square

 

[Mastermind01]

it can't be a square

So the answer is just $x = \sqrt{y^2 + 16}$ NOT $y+4$

 

[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 $x = ...$ ?

 

[sobergeek23]

why doesn't that reduce?

 

[BvU]

So the answer is just $x = \sqrt{y^2 + 16}$ NOT $y+4$

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

 

[sobergeek23]

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

 

[Mastermind01]

why doesn't that reduce?

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

 

[sobergeek23]

a^2+b^2

 

[BvU]

why doesn't that reduce?

It does reduce, but you have to be careful...

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

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'

 

[Mastermind01]

a^2+b^2

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

 

[G10rgos]

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.

 

[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.

 

[sobergeek23]

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

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

 

[sobergeek23]

is it aginst forum policy to give out answers?

 

[sobergeek23]

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

i couldn't find my other response but is it because the plus sign is there that we can't distribute the squared (x+y)^2 into x^2+y^2?

 

[BvU]

i couldn't find my other response but is it because the plus sign is there that we can't distribute the squared (x+y)^2 into x^2+y^2?

No. It is because it is not correct. Try a numerical example: (2+3) * (2+3)

 

[Ray Vickson]

is it aginst forum policy to give out answers?

Yes, absolutely. Helpers get reprimanded for doing it.

 

[BvU]

is it against forum policy to give out answers?

Very much so: there even are sanctions. For good reasons. We would get into trouble with teachers no end, for example.

From Info | terms and rules :

• Giving Full Answers:
  On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Complete solutions can be provided to a questioner after the questioner has arrived at a correct solution. If the questioner has not produced a correct solution, complete solutions are not permitted, whether or not an attempt has been made.

 

[BvU]

i couldn't find my other response but is it because the plus sign is there that we can't distribute the squared (x+y)^2 into x^2+y^2?

No. Because it isn't correct. Try e.g. (2+3)*(2+3) to see that.