Question:
If x − y = 7 and xy = 9, find the value of (x2 + y2).
Solution:
$x-y=7$
$\Rightarrow$ On squaring both the sides :
$\Rightarrow(x-y)^{2}=(7)^{2}$
$\Rightarrow x^{2}+y^{2}-2 x y=49$
$\Rightarrow x^{2}+y^{2}=49+2 x y$
Given:
$x y=9$
$\Rightarrow x^{2}+y^{2}=49+2(9)$
$\Rightarrow x^{2}+y^{2}=49+18$
$\Rightarrow x^{2}+y^{2}=67$
Therefore, the value of $x^{2}+y^{2}$ is 67 .
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