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

  • #1

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?
 

Answers and Replies

  • #2
BvU
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Quick answer: No.
Because your ##x^2 = (y+4)^2 \ne y^2+16 ##
 
  • #3
so whats the answer
 
  • #4
if i squared both sides it would just be the individual answer
 
  • #5
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What's the full problem statement ? 'Isolate' doesn't sound like a question with an answer ...
 
  • #6
that was the problem..it just said isolate the variable x..
 
  • #7
201
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NO! This is a fundamental mistake. ##\sqrt{a+b} \neq \sqrt{a} +\sqrt{b}##
 
  • #8
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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.
 
  • #9
said something like it is understood to be positive or something like that
 
  • #10
we were solving equations where you square both sides
 
  • #11
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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.
 
  • #12
it cant be a square
 
  • #13
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Poster has been reminded (too late) not to post answers to schoolwork questions on the PF
it cant be a square
So the answer is just ##x = \sqrt{y^2 + 16}## NOT ##y+4##
 
  • #14
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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
why doesnt that reduce?
 
  • #16
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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 :smile:
 
  • #17
learning experience means frustration and anger and deletion of account for me...
 
  • #18
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why doesnt that reduce?
Let's keep it cool. What's ##(a+b)^2##?
 
  • #19
a^2+b^2
 
  • #20
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why doesnt 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' :smile:
 
  • #21
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a^2+b^2
NO. Let's multiply it out. ##(a+b)(a+b)## Do you know the distributive law of multiplication?
 
  • #22
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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
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Hello G10, :welcome:

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
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?
 
Last edited by a moderator:
  • #25
is it aginst forum policy to give out answers?
 

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