Question 86

If the product of n positive real numbers is unity, then their sum is necessarily

Name: If the product of n positive real numbers is unity, then their sum is necessarily
Uploaded: Oct. 7, 2024, 4:50 p.m.
Duration: 1 min 4 s
Description: If the product of n positive real numbers is unity, then their sum is necessarily

Solution

Let the numbers be $$a_1,a_2....a_n.$$

Since the numbers are positive,

$$AM\geq GM$$

$$\frac{a_1+a_2+a_3....+a_n}{n}\geq (a_1*a_2....*a_n)^{1/n}$$

$$a_1+a_2+a_3....+a_n \geq n$$

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If the product of n positive real numbers is unity, then their sum is necessarily

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