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If A and G be the AM and GM between two numbers a,b then a,b are given by

A

(A+G)(A-G)

If H is the HM between a and b then,

(H-2a)(H-2b)=H²

(1/(H-a))+(1/(H-b))=(1/a)+(1/b)

((H+a)/(H-a))+((H+b)/(H-b))=2

If a,b,c are any numbers then,

a³+b³+c³-3abc=(a+b+c)(a+bw+cw²)(a+bw²+cw)

where w is cube root of unity.