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# help!

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If x^2 - y^2 = -12 and x + y = 6, find x and y.

Aug 25, 2018

#1
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We can make \(x^2 - y^2 = -12\) into \((x-y)(x+y) = -12\) by using “Difference of Squares”. Since we know that \(x+y = 6\), we can substitute that in. Now we have \(6(x-y) = -12\). We can divide \(6\) on both sides, which gives us \(x - y = -2\). We also still have the equation \(x + y = 6\). We can use elimination to get rid of \(x\). We will subtract the second equation from the first. This gives us \(-2y = -8\), so \(y = 4\). We can plug this back into any equation to get \(x\). So \(y = 4\) and \(x = 2\).

- Daisy

Aug 25, 2018
#2
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Thanks, Daisy !!!.....Just wanted to try this one , too....I like these kinds of problems ....

x^2  - y^2  = -12   and    x +  y  = 6   (1)

(x + y) ( x - y)  =  -12

6 ( x - y)  = -12

x - y  =  -2      (2)

Add (1)   and (2)   and we have that   2x  = 4  ⇒   x  = 2

And y =  2 + y  = 6   ⇒  y  = 4

So  (x ,y)  = ( 2, 4)

Aug 25, 2018
#3
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Yeah, they are fun!

- Daisy

dierdurst  Aug 25, 2018
#4
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I don't know how any math could be fun, but I'll take your word for it. Lol

Olpers  Aug 25, 2018
#5
+107656
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LOL!!!...we're just weird that way.....!!!!

CPhill  Aug 25, 2018