MathDB

Inequality

Source: 2005 National High School Mathematics League, Exam Two, Problem 2

March 20, 2020

inequalities

Problem Statement

Positive numbers

a, b, c, x, y, z

satisfy that

cy + bz = a

az + cx = b

, and

bx + ay = c

. Find the minimum value of the function

f(x,y,z) =\frac{x^2}{x+1}+\frac{y^2}{y+1}+\frac{z^2}{z+1}