GATE 2024 ST – Question 4

For x,y>0, ln((x+y)/2)=[ln x+ln y]/2. Find x/y+y/x.

Show answer and explanation

Correct answer: (C) 2

Explanation

Exponentiating gives (x+y)/2=√(xy), equality in arithmetic–geometric mean. Equivalently (√x−√y)²=0, so x=y. The requested sum is 1+1=**2, C**.

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