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For positive non-zero real variables p and q, if log(p² + q²) = log p + log q + 2 log 3, then, the value of (p⁴ + q⁴)/(p² q²) is

1. 79
2. 81
3. 9
4. 83

Correct answer: 79

Solution

The condition log(p^2+q^2) = log p + log q + 2log 3 gives p^2+q^2 = 9pq. Then (p^4+q^4)/(p^2q^2) = ((p^2+q^2)^2 - 2p^2q^2)/(p^2q^2) = (81p^2q^2 - 2p^2q^2)/(p^2q^2) = 79, option 0.

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