1, Cho $a,b\geq 0$.Chứng minh rằng: $(a+b)(ab+1)\geq 4ab$2, Cho $a,b,c\geq 0$. Chứng minh rằng: $(a+b+c)(ab+bc+ca)\geq 9abc$
3, Cho $a+b\geq 2$. Chứng minh rằng: $a^{3}+b^{3}\leq a^{4}+b^{4}$
4, Cho $z\geq y\geq x>0$. Chứng minh rằng:
$ y\times \left ( \frac{1}{x}+\frac{1}{z}\right )$$+\frac{1}{y}(x+z)$$\geq \left ( x+z \right )×$$\left ( \frac{1}{x} +\frac{1}{z}\right )$