Find $x^{2} + y^{2} if x + y = - 14 and x y = 84$

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Solution

Consider, $x^{2} + y^{2}$
$x + y = - 14$ , $x y = 84$
$\Rightarrow (x + y)^{2} = x^{2} + y^{2} + 2 x y$
$\Rightarrow x^{2} + y^{2} = (x + y)^{2} - 2 x y = (- 14)^{2} - 2 (84)$
$\Rightarrow 196 - 168 = 28$

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