If $a + b = 5$ and $a b = 6$ , then find $a^{2} + b^{2}$ .

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Solution

The correct option is D 13
Formula
${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
$=> a^{2} + b^{2} = {(a + b)}^{2} - 2 a b$
Given, $a + b = 5$ and $a b = 6$
So, $a^{2} + b^{2} = {(a + b)}^{2} - 2 a b = 5^{2} - 2 \times 6 = 25 - 12 = 13$

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