①√((a？ +b？ )/2)≥(a+b)/2≥√ab≥2/( 1/a+ 1/b).

②√(ab)≤(a+b)/2 .

③a？ +b？ ≥2ab .

④ab≤(a+b)？ /4。

⑤||a|-|b| |≤|a+b|≤|a|+|b| .

Principle:

① The inequality f (x): F(x) has the same solution.

② If the inequality f (x)

③ If inequality f (x): 0, inequality f (x)

④ inequality F(x)G(x)>0 and inequality have the same solution; Inequality f (x) g (x)