Given $(x + y) = 13$ and $x y = 22$ , find the value of $x^{2} + y^{2}$

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Solution

$x + y = 13$
$x y = 22$

Squaring bothside weget
.
$(x + y)^{2} = 13^{2} x^{2} + y^{2} + 2 x y = 169.$ .

Putting the value of $x y$ in

$x^{2} + y^{2} + 2 \times 22 = 169$

$x^{2} + y^{2} = 144 - 44 x^{2} + y^{2}$

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