MathDB

3

Part of 1998 Akdeniz University MO

Problems(2)

Inequality (easy)

Source: A book

1/30/2016
Let x,y,zx,y,z be non-negative numbers such that x+y+z≤3x+y+z \leq 3. Prove that
21+x+21+y+21+z≥3\frac{2}{1+x}+\frac{2}{1+y}+\frac{2}{1+z} \geq 3
inequalitieseasy inequality
inequality

Source:

1/31/2016
Let x,y,zx,y,z be real numbers such that, x≥y≥z>0x \geq y \geq z >0. Prove that x2−y2z+z2−y2x+x2−z2y≥3x−4y+z\frac{x^2-y^2}{z}+\frac{z^2-y^2}{x}+\frac{x^2-z^2}{y} \geq 3x-4y+z
inequalitieseasy inequalityeasy