CAT 2023 Progression Question (Hard)

Question

For some positive and distinct real numbers and , if is the arithmetic mean of and , then the relationship which will always hold true, is

Accepted Answer

We are given that y z x z x y . --- Step 1 Write arithmetic mean condition Arithmetic mean of and is x z x y 2 . So the given condition is y z x z x y 2 . --- Step 2 Simplify the equation Multiply both sides by 2 y z x z x y . Combine the terms on the right y z x y x z . Simplify numerator y z x y x

CAT 2023

Quantitative

Progression

Hard

For some positive and distinct real numbers $x, y$ and $z$ , if $\frac{1}{\sqrt{y}+\sqrt{z}}$ is the arithmetic mean of $\frac{1}{\sqrt{x}+\sqrt{z}}$ and $\frac{1}{\sqrt{x}+\sqrt{y}}$ , then the relationship which will always hold true, is

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