GATE 2021 ST – 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 p²/q²+q²/p².

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Correct answer: (B) 7

Explanation

Squaring the given identity gives p²/q²+2+q²/p²=9,so the formally requested value is **7, B**. The integer premise itself is inconsistent:the ratio p/q would have to be (3±√5)/2,which is irrational. The algebraic answer and official grading are preserved with this qualification.

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