Let 0 < z < y < x be three real numbers such that 1/x, 1/y, 1/z are in an arithmetic progression and x, √(2) y, z are in a geometric progression. If x y+y z+z x=3/(√(2)) x y z, then 3(x+y+z)² is equal to _ _ _ _ _ _.

Sequence and Series: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q46

JEE Main 20238 Apr, Evening shiftMathematicsMediumSequence and Series179× since 2002

Let

0 < z < y < x

be three real numbers such that

\frac{1}{x}, \frac{1}{y}, \frac{1}{z}

are in an arithmetic progression and

x, \sqrt{2} y, z

are in a geometric progression. If

x y+y z+z x=\frac{3}{\sqrt{2}} x y z

, then

3(x+y+z)^{2}

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.