Question

If $a,b,c$ are positive numbers in $A.P$., such that their product is $64$, then the minimum value of $b$ is equal to

• A. $2$
• B. $4$
• C. $1$
• D. $5$

Answer 1

Answer: (B)

Given $a+c=2b$
Also $\frac{a+b+c}{3}\ge \sqrt[3]{abc}$
$=\sqrt[3]{64}=4$
$\Rightarrow \frac{3b}{3}\ge 4$
$\Rightarrow b\ge 4$
$\Rightarrow$ minimum value of $b=4$