Question

if the sum of three positive numbers is a. find maximum value of their product. ​

Answer 1

Answer:

$x {3} + 6x^{2} + 8x$

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Step-by-step explanation:

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Answer 2

Answer:

MAX of product (x1)(x2)(x3)=$\frac{a^2}{9}$

Step by step explanation:

Consider 3 positive numbers be x1, x2, x3.

Given in the question,

                                    x1 + x2 + x3 = a

As we know from the relation, Arithmethic mean of n numbers is always greater than or equal to the geometric mean of those n numbers.

So,

                                  $\frac{(x1 + x2 +x3)}{3} \geq \sqrt{(x1 ) (x2) ( x3)}$

Substituting,               $\\ x1+x2+x3 =a$

On Squaring we get,

                                   $\\\frac{a^2}{9} \geq (x1 ) (x2) ( x3)$

Here we can see that the product of three number is less than or equal to  $\frac{a^2}{9}$

Hence, We can say that the maximum value of product of three number whose sum is a, is  $\frac{a^2}{9}$