1.Cho a,b,c > o và abc=1. Chứng minh $\frac{1}{1+b+c} + \frac{1}{1+a+c}+ \frac{1}{1+a+b }\leqslant 1$
2.Cho x+y+z = o; x,y,z $\epsilon [-1;1]$. Chứng minh $x^2+y^4+z^6\leqslant 2$
3.Cho a,b,c $\epsilon [0;1]$ .Chứng minh $a+b^2+c^3-ab-bc-ca\leqslant 1$
4.Cho x,y,z $\epsilon [0;2]$.Chứng minh $2(x+y+z)-(xy+yz+zx)\leqslant 4$
5.Cho x,y,z $\geqslant 0$; x+y+x $\leqslant 3$.Chứng minh $\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}\leqslant \frac{3}{2}\leqslant \frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}$
Edited by quynhly, 14-11-2015 - 23:02.