For some positive and distinct real numbers x x x , y y y , and z z z , if 1 x + z \frac{1}{\sqrt{x} + \sqrt{z}} x + z 1 is the arithmetic mean ...

CAT Medium Sequence & Series (AP, GP, HP) MCQ

Question

For some positive and distinct real numbers

x

y

, and

z

, if

\frac{1}{\sqrt{x} + \sqrt{z}}

is the arithmetic mean of

\frac{1}{\sqrt{x} + \sqrt{y}}

and

\frac{1}{\sqrt{y} + \sqrt{z}}

, then the relationship which will always hold true is:

\sqrt{x}, \sqrt{y}, \sqrt{z}

are in arithmetic progression

\sqrt{x}, \sqrt{z}, \sqrt{y}

are in arithmetic progression

y, z, x

are in arithmetic progression

x, y, z

are in arithmetic progression

cat 2023arithmetic meanprogressionalgebraic relationships

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