The product of n positive numbers is unity. T | vedclass

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(D) Given that the product of $n$ positive numbers $x_1, x_2, \dots, x_n$ is $1$,i.e.,$x_1 \cdot x_2 \cdot \dots \cdot x_n = 1$.According to the Arith

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Never less than $n$

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(D) Given that the product of $n$ positive numbers $x_1, x_2, \dots, x_n$ is $1$,i.e.,$x_1 \cdot x_2 \cdot \dots \cdot x_n = 1$.According to the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality,for any set of positive real numbers,the Arithmetic Mean is always greater than or equal to the Geometric Mean.$\frac{x_1 + x_2 + \dots + x_n}{n} \ge (x_1 \cdot x_2 \cdot \dots \cdot x_n)^{1/n}$.Substituting the given product value:$\frac{x_1 + x_2 + \dots + x_n}{n} \ge (1)^{1/n} = 1$.Therefore,$x_1 + x_2 + \dots + x_n \ge n$.This implies that the sum of these $n$ positive numbers can never be less than $n$.

The product of $n$ positive numbers is unity. Their sum is

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