Tag Archives: inequality

POTW113

August 16, 2013 – 10:40 pm

Find the smallest value of
\displaystyle \frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b}
as a, b and c range over the set of all positive real numbers.

This is problem 4 from the 2000 SMO Open Round 1.

By PC Toh | Posted in POTW | Also tagged , | Comments (2)

POTW104

June 14, 2013 – 2:41 pm

Let n be a positive integer, and let a_1, a_2, \ldots, a_n be positive real numbers such that a_1 + a_2 + \cdots + a_n =1. Is it true that
\displaystyle \frac{a_1^4}{a_1^2+ a_2^2} + \frac{a_2^4}{a_2^2+ a_3^2} + \cdots + \frac{a_{n-1}^4}{a_{n-1}^2+ a_n^2} + \frac{a_n^4}{a_n^2+ a_1^2} \ge \frac{1}{2n} ?
Justify your answer.

This is problem 2 from the 2001 SMO Open Round 2.

By PC Toh | Posted in POTW | Also tagged , , | Comments (2)