Question

If product of $n$ positive numbers is unity. The sum of these numbers can not be less than

• A. $1$
• B. $n$
• C. $n+1$
• D. $2$

Answer 1

The correct option is B $n$

We know $A.M.\ge G.M$
So, $\frac{x_1+x_2+\cdots +x_n}{n}\ge \sqrt[n]{n{x}_1{x}_2\cdots x_n}$
Given: $x_1{x}_2\cdots x_n=1$
Hence, $\frac{x_1+x_2+\cdots +x_n}{n}\ge 1$
$\Rightarrow x_1+x_2+\cdots +x_n\ge n$