Question

If the product of $n$ positive real numbers is $1$, what is the minimum value of their sum?

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

Answer 1

The correct option is C $n$

We know if we have $n$ real numbers $x_1,x_2,.......,x_n$, then

$AM\ge GM$ ........ $\left(1\right)$

$\frac{x_1+x_2+x_3....+x_n}{n}\ge \sqrt[n]{n{x}_1{x}_2.....x_n}$

Now it is given that the product of n real no. is $1$ i.e$x_1{x}_2.....x_n=1$

$\Rightarrow$ $\frac{x_1+x_2+....+x_n}{n}\ge 1$

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

So, the minimum value of $(x_1+x_2+..........+x_n)$ is $n$

Hence, option C is correct.