Question:
If x − y = 7 and xy = 9, find the value of x2 + y2
Solution:
We have:
$(x-y)^{2}=x^{2}-2 x y+y^{2}$
$\Rightarrow x^{2}+y^{2}=(x-y)^{2}+2 x y$
$\Rightarrow x^{2}+y^{2}=7^{2}+2 \times 9 \quad(\because x-y=7$ and $x y=9)$
$\Rightarrow x^{2}+y^{2}=7^{2}+2 \times 9$
$\Rightarrow x^{2}+y^{2}=49+18$
$\Rightarrow x^{2}+y^{2}=67$
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