Find the value of ab, when $a - b = 3$ and $a^{2} + b^{2} = 15.$

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Solution

The correct option is C
3

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

$2 a b = a^{2} + b^{2} - (a - b)^{2} = 15 - (3)^{2} = 15 - 9 = 6$

So, ab $= \frac{1}{2} \times 2 a b = \frac{1}{2} \times 6 = 3$

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