Question:
If x + y = 12 and xy = 14, find the value of (x2 + y2).
Solution:
$x+y=12$
On squaring both the sides:
$\Rightarrow(x+y)^{2}=(12)^{2}$
$\Rightarrow x^{2}+y^{2}+2 x y=144$
$\Rightarrow x^{2}+y^{2}=144-2 x y$
Given:
$x y=14$
$\Rightarrow x^{2}+y^{2}=144-2(14)$
$\Rightarrow x^{2}+y^{2}=144-28$
$\Rightarrow x^{2}+y^{2}=116$
Therefore, the value of $x^{2}+y^{2}$ is 116 .
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