Question

if a is the arithmetic mean between a and b then prove that a+2a/a-b+a+2b/a-a=4

Answer 1

A= (a+b)/2  

A-b= (a+b)/2 - b = (a-b)/2  

A-a = (b-a)/2 = -(a-b)/2  

Now,  

(A+2a)/(A-b) + (A+2b)/(A-a)  

= 2*(A+2a)/(a-b) - 2*(A+2b)/(a-b)  

=(2A+4a-2A-4b)/(a-b)  

=(4a-4b)/(a-b)  

= 4*(a-b)/(a-b)  

=4