130

Part of 1970 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 130 All Soviet Union MO 1970 abc=1, a+b+c > (1/a+1/b+1/c) >0

Source:

The product of three positive numbers equals to one, their sum is strictly greater than the sum of the inverse numbers. Prove that one and only one of them is greater than one.

algebrainequalities