If $x + y = 7$ and $x y = 12$ , find $x^{2} + y^{2}$ .

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Solution

Using the given identity $x + y = 7$ and $x y = 12$
$\Rightarrow$ $(7)^{2}$ = $x^{2} + 2 (12) + y^{2}$
$\Rightarrow$ $49$ = $x^{2} + 24 + y^{2}$
$\Rightarrow$ $49 - 24$ = $x^{2} + y^{2}$
$\Rightarrow$ $x^{2} + y^{2}$ = $25$
Hence the answer is $x^{2} + y^{2} = 25$

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