Question

If arithmetic mean and geometric mean of two positive numbers $a$ and $b$ are 7 and $\sqrt{6}$ respectively, then the value of $\left(a^3-15 a^2+20 a-5\right)$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

$ \frac{ a + b }{2}=7, ab =6$
$\Rightarrow b =\frac{6}{ a } \Rightarrow a ^2+6-14 a =0 $
$\Rightarrow a \left( a ^2-14 a +6\right)-1\left( a ^2-14 a +6\right)+1$
$\Rightarrow 1$