If $x - y = 5$ and $x y = 12,$ find the value of $x^{2} + y^{2} .$

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Solution

Finding the value of the given expression:
$x - y = 5 - - - - - - (1)$
On squaring both sides we get,
${(x - y)}^{2} = 25 x^{2} + y^{2} - 2 x y = 25 (U \sin g {(a - b)}^{2} = a^{2} - 2 a b + b^{2}) x^{2} + y^{2} = 25 + 2 x y x^{2} + y^{2} = 25 + 2 \times 12 (A s, x y = 12 g i v e n i n t h e q u e s t i o n) x^{2} + y^{2} = 25 + 24 x^{2} + y^{2} = 49$
Hence, value of the expression $x^{2} + y^{2}$ is $49 .$

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