Question

State true or false:

If $a_1,a_2,a_3\in +R$, then $3a_1{a}_2{a}_3\le a_1^3+a_2^3+a_3^3$

• A. True
• B. False

Answer 1

The correct option is A True

we know that $A.M.\ge G.M.$

$⟹\frac{a_1^3+a_2^3+a_3^3}{3}\ge \sqrt[3]{3a_1^3\ast a_2^3\ast a_3^3}$

$⟹\frac{a_1^3+a_2^3+a_3^3}{3}\ge \sqrt[3]{3(a_1\ast a_2\ast a_3{)}^3}$

$⟹\frac{a_1^3+a_2^3+a_3^3}{3}\ge a_1\ast a_2\ast a_3$

$⟹a_1^3+a_2^3+a_3^3\ge 3a_1{a}_2{a}_3$