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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
+2532
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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