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GATE 2021 ES – Question 2

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

Positive integers p, q satisfy $p/q+q/p=3$. Find $p^2/q^2+q^2/p^2$.

  1. 3
  2. 7
  3. 9
  4. 11

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Show answer and explanation

Correct answer: (B) 7

Explanation

Squaring the supplied relation gives $p^2/q^2+q^2/p^2+2=9$, so the intended answer is **7, B**. There is a source qualification: no positive integers meet the premise, since p/q would solve r²−3r+1 = 0 and be irrational. The algebraic result holds if positive real values were intended.

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