1. Cho a,b>0, a+b=2. CMR: $ab\leq a^{a}b^{b}$
2. Cho a,b,c dương thỏa mãn a+b+c=1.CMR:
a. $\frac{1}{3^{a}}+\frac{1}{3^{b}}+\frac{1}{3^{c}}\geq 3(\frac{a}{3^{a}}+\frac{b}{3^{b}}+\frac{c}{3^{c}})$
b. $\sqrt[3]{a+b}+\sqrt[3]{c+b}+\sqrt[3]{a+c}\leq \sqrt[3]{18}$
3. Cho a,b,c dương.CMR: $\sqrt{a^2-ab+b^2}+\sqrt{b^2-bc+c^2}+\sqrt{c^2-ac+a^2}\geq a+b+c$
4. Cho a,b,c dương thỏa mãn abc=1. CMR:
a.$(a+\frac{1}{b}-1)(b+\frac{1}{c}-1)(c+\frac{1}{a}-1)\leq 1$
b. $a^{3}+b^{3}+c^{3} \geq a+b+c$
c. $a^{3}+b^{3}+c^{3} \geq $a^2+b^2+c^2