MathDB

(a) Show that if

x

and

y

are positive real numbers, then

(x+y)^5\ge 12xy(x^3+y^3)

(b) Prove that the constant

12

is the best possible. In other words, prove that for any

K>12

there exist positive real numbers

x

and

y

such that

(x+y)^5<Kxy(x^3+y^3)

Problem Statement