I. Basic inequality

√(ab)≤(a+b)/2, then it can be changed into the square of the average value of a 2-2ab+b 2 ≥ 0, a 2+b 2 ≥ 2ab, AB≤A and B.

Second, the absolute inequality formula

| |a|-|b| |≤|a-b|≤|a|+|b| .

| |a|-|b| |≤|a+b|≤|a|+|b| .

Third, Cauchy inequality.

Let a 1, a2, an, b 1, b2 and bn all be real numbers, then (a1b1+a2b2+anbn) 2 ≤ (a12+a22+an2) *.

Fourthly, triangle inequality.

For the reinforced inequality of any two vectors b, this inequality can also be called the triangular inequality of vectors.

Five, quadrilateral inequality

If for any a 1 ≤ a2