If $a - b = 5$ and $a^{2} + b^{2} = 53$ , then find the value of $a b$ .

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Solution

Given that, $a - b = 5$ and $a^{2} + b^{2} = 53$

We know that $(a - b)^{2} = a^{2} + b^{2} - 2 a b$

$⟹ (5)^{2} = 53 - 2 a b$

$⟹ 25 = 53 - 2 a b$

$⟹ 2 a b = 53 - 25$

$⟹ 2 a b = 28$

$⟹ a b = \frac{28}{2}$

$∴ a b = 14$ (Ans)

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