If $x + y = 12$ and $x y = 32$ , find the value of $x^{2} + y^{2}$ .

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Solution

The correct option is A 80

Since ${(x + y)}^{2} = x^{2} + y^{2} + 2 x y$

$144 = x^{2} + y^{2} + 2 \times 32$ [Substituting x + y = 12 and xy = 32]

$144 - 64 = x^{2} + y^{2}$

$x^{2} + y^{2} = 80$
Hence, $x^{2} + y^{2} = 80$

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