1) Cho a, b, c > 0 thỏa mãn a+b+c=3. Chứng minh rằng: $\frac{a}{a+bc}+\frac{b}{b+ca}+\frac{c}{c+ab}\geq\frac{3}{2}$
2) Cho a, b, c, d > 0. Chứng minh rằng: $\frac{1}{a^2+ab}+\frac{1}{b^2+bc}+\frac{1}{c^2+cd}+\frac{1}{d^2+da}\geq\frac{4}{ac+bd}$
3) Cho a, b, c > 0. Chứng minh rằng: $\frac{1}{a\sqrt{3a+2b}}+\frac{1}{b\sqrt{3b+2c}}+\frac{1}{c\sqrt{3c+2a}}\geq\frac{3}{\sqrt{5abc}}$
4) Cho a, b, c > 0. Chứng minh rằng: $\sqrt{(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})}\geq 1+\sqrt{1+\sqrt{(a^2+b^2+c^2)(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2})}}$