Question

Product of n positive numbers is unity. 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 such that

$x_1\times x_2\times ----\times x_n=1$ ...(1)
Now, $\because A.M.\ge G.M.$

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

$\Rightarrow x_1+x_2+.....+x_n\ge n$ by (1)