1, general form
(∑ai^2)(∑bi^2)≥(∑ai bi)^2。
The equal sign holds as follows: a1:b1= a2: B2 = … = an: bn, or both ai and bi are zero.
2. Two-dimensional form
(a^2+b^2)(c^2 + d^2)≥(ac+bd)^2。
Equal sign condition: ad=bc.
3. Vector form
|α||β|≥|α β|,α=(a 1,a2,…,an),β=(b 1,b2,…,bn)(n∈N,n≥2)。
The condition of equal sign is that β is zero vector, or α = λ β (λ∈ r).
4. Triangle type
√(a^2+b^2)+√(c^2+d^2)≥√[(a-c)^2+(b-d)^2]。
Equal sign condition: ad=bc.