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If x - y = 3 and x^2 - y^2 = 63, then find x^2 + y^2.

 Jun 20, 2020
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x^2-y^2 is the difference of squares: (x+y)(x-y)

 

So (x+y)(x-y)=63

We already know x-y=3.

 

3(x+y)=63

x+y=21

 

We can form a system of equations from this.

x-y=3

x+y=21

 

We solve and find that x=12 and y=9.

 

So x^2+y^2=12^2+9^2=144+81=225.

 Jun 20, 2020

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