Cho a, b, c thuộc R. CM:
1, \(ab\le\left(\dfrac{a+b}{2}\right)^2\le\dfrac{a^2+b^2}{2}\)
2, \(\dfrac{a^3+b^3}{2}\ge\left(\dfrac{a+b}{2}\right)^3\)
3, \(a^4+b^4\ge a^3b+ab^3\)
4, \(a^4+3\ge4a\)
5, \(a^3+b^3+c^3\ge3abc\left(a,b,c>0\right)\)
6, \(a^4+b^4\le\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}\left(a,b\ne0\right)\)
7, \(\dfrac{1}{1+a^2}+\dfrac{1}{1+b^2}\ge\dfrac{2}{1+ab}\left(a,b\ge1\right)\)
8, \(\left(a^5+b^5\right)\left(a+b\right)\ge\left(a^4+b^4\right)\left(a^2+b^2\right)\)