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GATE 2024 CS (CS1) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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 $\frac{p^4+q^4}{p^2q^2}$ is

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

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Correct answer: (A) 79

Explanation

$p^2+q^2=9pq$. Then $(p^2+q^2)^2=81p^2q^2$, so $p^4+q^4=79p^2q^2$; ratio is 79.