If $64 a^{2} + 36 b^{2} = 400, a b = 4$ , then $8 a + 6 b$ is:

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None of the above

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Solution

The correct option is D 28
Given $64 a^{2} + 36 b^{2} = 400, a b = 4$
We know
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
therefore,
$(8 a + 6 b)^{2} = (8 a)^{2} + (6 b)^{2} + 2 (8 a) (6 a)$
$= 64 a^{2} + 36 b^{2} + 96 a b$
$= 400 + 96 \times 4$
$= 400 + 384$
$(8 a + 6 b)^{2} = 784$
$8 a + 6 b = \sqrt{784}$
$8 a + 6 b = 28$

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