Question

The sum of three number is constant. Prove that their product is maximum when they are
equal.

Answer 1

Step-by-step explanation:

Answer ⤵️

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positive numbers x, y, and z, whose sum has the constant value S, is a maximum when the three numbers are equal. Use this result to prove that ∛xyz ≤ x + y + z / 3.

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Answer 2

Answer:

the three numbers product is maximum when they are

equal.

Step-by-step explanation:

given that:

The sum of three numbers is constant.

let the numbers be a , b , c

we have to prove that :

product is maximum when the three numbers are equal.

using the formula :

$\sqrt[3]{abc}\leq (a+b+c)/3$

proof:

three numbers are equal. so , a = b = c = a

the formula becomes:

$\sqrt[3]{(a)(a)(a)} \leq (a + a +a)/3$

$\sqrt[3]{a^3} \leq (3a)/3$

a ≤ a

conclusion:

the three numbers product is maximum when they are

equal.