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If x+y=9 and xy=10, what is the value of \(x^2 + y^2\)?

 Apr 26, 2022
 #1
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x^2 + y^2 = 72.

 Apr 26, 2022
 #2
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Note that \(x^2+y^2=(x+y)^2-2xy\)

 

Substituting what we know, we have: \(x^2+y^2=9^2-2 \times 10\)

 

Solving this, we find: \(x^2+y^2=\color{brown}\boxed{61}\)

 Apr 26, 2022

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