3

Part of 2003 India Regional Mathematical Olympiad

Problems(1)

Source: Indian RMO 2003 Problem 3

a,b,c

be three positive real numbers such that

a + b +c =1

. prove that among the three numbers

a-ab, b - bc, c-ca

there is one which is at most

\frac{1}{4}

and there is one which is at least

\frac{2}{9}