If $a - b = 4$ and $a + b = 6$ , then find $a b$

5

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2

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45

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3

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Solution

The correct option is D $5$
Given, $a + b = 6$

Squaring both sides, we get

$(a + b)^{2} = 6^{2}$

$=> a^{2} + b^{2} + 2 a b = 36$ ------------(i)

Also $a - b = 4$

Squaring both sides, we get

$(a - b)^{2} = 4^{2}$

$=> a^{2} + b^{2} - 2 a b = 16$ ------------(ii)

(i) $-$ (ii), we get

$=> (a^{2} + b^{2} + 2 a b) - (a^{2} + b^{2} - 2 a b) = 36 - 16$

$=> 4 a b = 20$

$=> a b = 5$

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