6

Part of 1982 Spain Mathematical Olympiad

Problems(1)

u^a v^b <= au + bv if u,v>=0 a,b>0 with a+b=1

Source: Spanish Mathematical Olympiad 1982 P6

u, v

are any nonnegative real numbers, and

a,b

positive real numbers such that

a + b = 1

u^a v^b \le au + bv.

algebrainequalities