a^2+b^2 ≥ 2ab

√(ab)≤(a+b)/2 ≤(a^2+b^2)/2

a^2+b^2+c^2≥(a+b+c)^2/3≥ab+bc+ac

A+b+c≥3× cubic radical abc

certificate

There are many methods to prove mean inequality, such as mathematical induction (first mathematical induction or backward induction), Lagrange multiplier method, Qinsheng inequality method, rank inequality method, Cauchy inequality method and so on. Here is a brief introduction to the proof method of mathematical induction: (note: it is the proof method of N-dimensional mean inequality) It needs an auxiliary conclusion to prove by mathematical induction.