Quick question: x^2-y^2=16 (find 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.

 

[sobergeek23]

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.

thats stupid because I am my post under my attempt i obviously did try..i only asked for an answer when you made your response complicated..anyway in your last post you said "no because it isn't correct" gee thanks for the help...helpful wouldve been if you posted whatever rule made it not correct..

 

[vantroff]

Because how the distributive, associative and commutative properties work. And where they work. (at least that what I think)

(ab)² = a²b²
Why? Because (ab)² means (ab)*(ab)=ab*ab=aa*bb=a²b²
But,

(a+b)² = (a+b)(a+b)=a(a+b)+b(a+b)=a²+ab+ba+b²=a²+2ab+b² ≠ a²+b²

We can think for the thing in the parentheses like x.
x=a+b
So, x^2=x*x=(a+b)(a+b)

I hope I didn't made some mistake...

 

[BvU]

thats stupid because I am my post under my attempt i obviously did try..i only asked for an answer when u made ur response complicated..anyway in ur last post u said "no because it isn't correct" gee thanks for the help...helpful wouldve been if u posted whatever rule made it not correc

I don't mind being shown wrong, but I don't like being called stupid. I did not just say it was incorrect, I even gave you an example where you could see for yourself that $(2+3) * (2+3) \ne 2^2 + 3^2$.

I tried to help you and apparently failed. So I give up and leave it to others -- if any -- to help you with your problems.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

is it aginst 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.

thats stupid because I am my post under my attempt i obviously did try.

It is definitely our policy here, and is clear in the PF rules (under INFO at the top of the page) that you agreed to when joining here. One of our most important themes here at the PF is to help students learn how to learn. That means that our tutorial help efforts are limited to finding mistakes, asking questions, giving hints, etc. But posting the answer is strictly forbidden here.

You were very close to figuring out the answer on your own with their hints and the mistakes that they found and pointed out. I especially like the post that showed you an example multiplication to try to see where your misunderstanding was.

I don't mind being shown wrong, but I don't like being called stupid

I don't think the OP was calling you stupid, I think she was saying that the PF policy of not giving students answers is stupid. Not the first time a student has posted that...

 

[berkeman]

After a *lot* of cleanup and reminding some posters not to post answers to homework questions at the PF, the thread is re-opened. The OP may have what she needs for her homework, or she may have clarifying questions still.

 

[Kaura]

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?

Suppose we have a square with side length a+b then the area would be (a+b)²
In this high quality graphic suppose that the red part of the side length is a and the blue is b
What would the total area be?