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= {3}/{\sqrt{2}} x y z, then 3(x+y+z)^2 is equal to _______. [8-Apr-2023 shift 2]

Sequences and Series Part 2

Section: Mathematics

Question : 2 of 100

Marks: +1, -0

Let 0<z<y<x be three real numbers such that ‌

,‌

are in an arithmetic progression and x,√2y,z are in a geometric progression. If xy+yz+zx=‌

√2

xyz, then 3(x+y+z)2 is equal to _______.

[8-Apr-2023 shift 2]

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