If $x + y = 12$ and $x y = 14$ , find the value of $(x^{2} + y^{2})$

113

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64

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116

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183

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Solution

The correct option is C $116$
Given, $x + y = 12$ and $x y = 14$
$x + y = 12$
Squaring both sides, we get,
$(x + y)^{2} = 12^{2}$
$=> x^{2} + y^{2} + 2 x y = 144$
$=> x^{2} + y^{2} + 2 (14) = 144$
$=> x^{2} + y^{2} = 144 - 28$
$=> x^{2} + y^{2} = 116$

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