For positive non-zero real variables p and q, if (p^2 + q^2) = p + q + 2 3, then, the value of p^4 + q^4p^2 q^2 is

GATE CSE 2024 Session 1 Q5: Value of (p⁴ + q⁴)/(p²q²) from a log equation

For positive non-zero real variables $p$ and $q$ , if

$\log(p^2 + q^2) = \log p + \log q + 2\log 3,$

then, the value of $\dfrac{p^4 + q^4}{p^2 q^2}$ is

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Answer: A (official GATE 2024 final answer key)

Concept used: Combine logarithms, then use $(p^2 + q^2)^2 = p^4 + q^4 + 2p^2q^2$ .

First step: The equation gives $p^2 + q^2 = 9pq$ ; square both sides.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key