MathDB

SRMC 2010 P3

Source:

December 7, 2015

inequalities

Problem Statement

For positive real numbers

a, b, c, d,

satisfying the following conditions:

a(c^2 - 1)=b(b^2+c^2)

and

d \leq 1

, prove that :

d(a \sqrt{1-d^2} + b^2 \sqrt{1+d^2}) \leq \frac{(a+b)c}{2}