MathDB

5

Part of 2009 China Northern MO

Problems(1)

sum (x^{2009}-2008(x-1))/(y+z) >= 1/2 (x+y+z), if x,y,z>0, x^2+y^2+z^2 = 3

Source: China Northern MO 2009 p5 CNMO

12/12/2020
Assume : x,y,z>0x,y,z>0 , x2+y2+z2=3 x^2+y^2+z^2 = 3 . Prove the following inequality : x2009−2008(x−1)y+z+y2009−2008(y−1)x+z+z2009−2008(z−1)x+y≥12(x+y+z){\frac{x^{2009}-2008(x-1)}{y+z}+\frac{y^{2009}-2008(y-1)}{x+z}+\frac{z^{2009}-2008(z-1)}{x+y}\ge\frac{1}{2}(x+y+z)}
algebrainequalities