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GATE 2024 CS (CS2) – Question 4

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

For positive non-zero real variables $x$ and $y$, if $\ln\left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln(x)+\ln(y)]$, then, the value of $\frac{x}{y}+\frac{y}{x}$ is

  1. 1
  2. 1/2
  3. 2
  4. 4

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Correct answer: (C) 2

Explanation

AM = GM implies x = y, so x/y + y/x = 1 + 1 = 2.