If $a + b = 10, a b = 24$ , find $a^{2} + b^{2}$

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Solution

Consider the following question.

$a + b = 10, a b = 24, a^{2} + b^{2} =$

${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

${(10)}^{2} = a^{2} + b^{2} + 2 * 24$

$100 = a^{2} + b^{2} + 48$

$a^{2} + b^{2} = 52$

Hence, this is the required answer.

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