Question

Let 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. $\frac{1}{2}$
• D. none of these

Answer 1

Answer: (B)

2

$x$ is the A.M between $a$ and $b$
$\Rightarrow x=\frac{a+b}{2}$ ...(1)
and $y,z$ is the G.M between $a$ and $b$
Therefore, $a,y,z,b$ are in G.P
$\Rightarrow y^2=az$ $\Rightarrow y^3=ayz$
and $\Rightarrow z^2=by$ $\Rightarrow z^3=byz$
Now, $\frac{y^3+z^3}{xyz}=\frac{(a+b)yz}{xyz}$
From (1), we get
$\frac{y^3+z^3}{xyz}=2$
Ans: B