Question

If the product of $n$ positive numbers is unity, then the sum of these numbers can not be less than

• A. $2n$
• B. $n$
• C. $n+1$
• D. $n+7$

Answer 1

The correct option is B $n$

We know $A.M.\ge G.M$
$\frac{x_1+x_2+\cdots +x_n}{n}\ge \sqrt[n]{n{x}_1{x}_2\cdots x_n}(\because x_1{x}_2\cdots x_n=1)\Rightarrow \frac{x_1+x_2+\cdots +x_n}{n}\ge 1\therefore x_1+x_2+\cdots +x_n\ge n$