Question

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

• A. $y$
• B. $2y$
• C. $2xyz$
• D. None of these

Answer 1

The correct option is B

$2y$

Explanation for the correct option:

Find the value of $\mathit{x}\mathbf{+}\mathit{z}$:

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

Let $a^{1/x}=b^{1/y}=c^{1/z}=k$

So, $a=k^x,b=k^y,c=k^z$

Given $b^2=ac$

$$\begin{gathered} \Rightarrow k^{2y}=\left(k^x\right)\left(k^z\right) \\ \Rightarrow k^{2y}=k^{(x+z)} \\ \Rightarrow 2y=x+z \\ \Rightarrow x+z=2y \end{gathered}$$

Hence, the correct option is (B).