If-a-4-b-4-c-4-d-4-16-Prove-that-a-5-b-5-c-5-d-5-32-

Question Number 75883 by TawaTawa last updated on 19/Dec/19

If a^{4} + b^{4} + c^{4} + d^{4} = 16

Prove that, a^{5} + b^{5} + c^{5} + d^{5} ⩽ 32

Commented by prakash jain last updated on 19/Dec/19

a^{4} ⩽ 16

\Rightarrow - 2 ⩽ a ⩽ 2

a, b, c, d all lie in range [- 2, 2]

\Rightarrow a^{5} + b^{5} + c^{5} + d^{5}

⩽ 2 (a^{4} + b^{4} + c^{4} + d^{4}) = 32

Commented by TawaTawa last updated on 23/Dec/19

God bless you sir