Properties of arithmetic, geometric, and harmonic means between two given numbers (a and b)

A.M. = A = (a+b)/2
G.M. = G = √ab
H.M. = H = 2ab/(a+b)

1. A≥G≥H
2. A,G,H form a GP, i.e., G² = AH
3. The equation x²-2Ax+G² has as its roots a and b.
4. The equation x³-3A x²+3G³x/H-G³ = 0 has as its roots a,b,c when A,G,and H are arithmetic mean, geometric mean, and harmonic mean of three numbers a,b,and c.