If $a^{2} + b^{2} = 14$ and $a b = 3$ , find the value of $2 (a + b)^{2} - 5 (a - b)^{2}$ .

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Solution

The correct option is B
0

$\Rightarrow 2 (a + b)^{2} - 5 (a - b)^{2}$ .

$= 2 (a^{2} + b^{2} + 2 a b) - 5 (a^{2} - 2 a b + b^{2})$
$= 2 a^{2} + 2 b^{2} + 4 a b - 5 a^{2} + 10 a b - 5 b^{2}$
$= - 3 a^{2} - 3 b^{2} + 14 a b$
$= - 3 (a^{2} + b^{2}) + 14 a b$
$= (- 3 \times 14) + (14 \times 3)$
$= - 42 + 42$
$= 0$

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