Mean inequality, also known as mean inequality, is an important formula in mathematics, that is, harmonic mean does not exceed geometric mean, geometric mean does not exceed arithmetic mean, and arithmetic mean does not exceed square mean. Mean inequality can also be regarded as the inference that "for several non-negative real numbers, their arithmetic mean is not less than geometric mean".

The content of the formula is Hn≤Gn≤An≤Qn, that is, the harmonic average does not exceed the geometric average, the geometric average does not exceed the arithmetic average, and the arithmetic average does not exceed the square average.

The derivation process of mean inequality;

∵ (a-b) =a？ -2ab+b？ ≧0; ∴a？ +b？ The 2ab equal sign holds (a, b∈R) if and only if a = b.

√(√m-√n)？ = m-2√(Mn)+n≧0； ∴m+n≧2√(mn)； The equal sign holds (m, n∈R+) if and only if m = n.

High school means inequality: a? +b？ ≥2ab； √(ab)≤(a+b)/2； Answer? +b？ +c？ ≥(a+b+c)？ /3; A+b+c≥3× cubic radical abc.