If a^ 1/x = b^ 1/y = c^ 1/z and b^2 = ac then x + z = - Vidyadip

MCQ

If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and ${b^2} = ac$ then $x + z = $

A
$y$
✓
$2y$
C
$2xyz$
D
None of these

✓

Answer

Correct option: B.

$2y$

b
(b) ${a^{1/x}} = {b^{1/y}} = {c^{1/z}} = k\,({\rm{say}}) \Rightarrow a = {k^x},\,b = {k^y},\,c = {k^z}$

${b^2} = ac \Rightarrow {({k^y})^2} = {k^x}.{k^z}$ $ \Rightarrow $ ${k^{2y}} = {k^{x + z}} \Rightarrow x + z = 2y$.

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