Statement 1: If x+ x= y+ 1y , x [0, ], then x= 4 , y=1. Statement 2: AM GM.

JEE Main Mathematics question

Statement 1: If , , then , . Statement 2: AM GM.

(A)Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1Correct
(B)Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1
(C)Statement 1 is True, Statement 2 is False
(D)Statement 1 is False, Statement 2 is True

Answer: (A)

By AM–GM, for , so the right side is at least . The left side satisfies . Equality on both sides forces

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Question ID VK-008170