Which of the following options correctly match, when the subject of the given formula is change to m?

2p = 3q + $\sqrt{5 p^{2} - m}$

p² + 8q² + 15 pq

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2p² – 4q² + 16 pq

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2p² – 5q² + 12 pq

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p² – 9q² + 12 pq

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Solution

The correct option is D
p² – 9q² + 12 pq

$2 p = 3 q + \sqrt{5 p^{2} - m} (2 p - 3 q)^{2} = (5 p^{2} - m) m = 5 p^{2} - (2 p - 3 q)^{2} m = 5 p^{2} - (4 p^{2} + 9 q^{2} - 12 p q) m = p^{2} - 9 q^{2} + 12 p q$

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