Question

if A is the AM between a and b prove that

[a] (A+2a)/(A-b) + (A+2b)/(A-a) =4

[b] A-b=(b-a)^2

Answer 1

A=a+b2.A=a+b2. So

a+b2+2aa+b2−b+a+b2+2ba+b2−aa+b2+2aa+b2−b+a+b2+2ba+b2−a

=5a+ba−b+a+5b−a+b=5a+ba−b+a+5b−a+b

=5a+ba−b−a+5ba−b=5a+ba−b−a+5ba−b

=4a−4ba−b=4a−4ba−b

=4