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Multiplication of Rational Expressions

If x-y=7 an...

Question

If $x - y = 7$ and $x y = 8$ find the value of $(x^{2} + y^{2})$ .

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Solution

$x - y = 7$
$\Rightarrow (x - y)^{2} = 49$
$\Rightarrow x^{2} + y^{2} - 2 x y = 49$
$\Rightarrow x^{2} + y^{2} = 49 + 2 (8) = 49 + 16 = 65$

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