Given that $x - y = 8, x y = 2$ . Find $x^{2} + y^{2}$ .

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Solution

$x - y = 8, x y = 2$
we know that
${(x - y)}^{2} = x^{2} + y^{2} - 2 x y \Rightarrow {(8)}^{2} = x^{2} + y^{2} - 2 \times 2 \Rightarrow 64 = x^{2} + y^{2} - 4 \Rightarrow x^{2} + y^{2} = 64 + 4 \Rightarrow x^{2} + y^{2} = 68$

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