If $x - y = 7$ and $x y = 9$ find the value of $(x^{2} + y^{2})$

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Solution

$x - y = 7; x y = 9$
As we know
$(x - y)^{2} = x^{2} + y^{2} - 2 x y$
$7^{2} = x^{2} + y^{2} - 2 (9)$
$49 + 18 = x^{2} + y^{2}$
$67 = x^{2} + y^{2}$

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