Question

If $x$ be the AM and $y,z$ be two GMs between two positive numbers, then $\frac{y^3+z^3}{xyz}$ is equal to.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Let the two numbers are $a$ and $b$
$\therefore a,x,bϵ$ A.P $\Rightarrow x=\frac{a+b}{2}..\left(1\right)$
and $a,y,z,bϵ$ G.P $\Rightarrow \frac{y}{a}=\frac{z}{y}=\frac{b}{z}..\left(2\right)$
Hence, $\frac{y^3+z^3}{xyz}=\frac{1}{x}(\frac{y^2}{z}+\frac{z^2}{y})=\frac{1}{x}(a+b)=2$ using (1) and (2).