Question

Product of $n$ positive numbers is unit. The sum of these numbers can not be less than

• A. $1$
• B. $n$
• C. $n^2$
• D. None of these

Answer 1

The correct option is B $n$

Let $x_1,x_2,....x_n$ are $n$ positive numbers.

Given $x_1,x_2,x_3....x_n=1$

Now, since $A.M.\ge G.M.$

$\Rightarrow \frac{x_1+x_2+......+x_n}{n}\ge {(x_1\times x_2\times .....\times x_n)}^{1/n}$

$\Rightarrow x_1+x_2+......+x_n\ge n$