If `A` is the A.M. between `a and b,` prove that `(A+2a)/(A-b)+(A+2b)/(A-a)=4.`

If A is the A.M. between a and b, prove that : 4(a-A)(A-b)=(a-b)^(2) .

If A is the A.M. between a and b, prove that : (A-a)^(2) +(A-b)^(2)=1/2(a-b)^(2) .

In sub - part (i) to (x) choose the correct option and in sub - part (xi) to (xy), answer the questions as intructed . If A is the A.M between a and b , then (A+2a)/(A-b)+(A+2b)/(A-a)=

If A is the A.M between a and b prove that : (i) (A-a)^(2)+(A-b)^(2)=1/2(a-b)^(2) (ii) 4(a-A)(A-b)=(a-b)^(2)

If A_1 and A_2 are two A.M.’s between a and b, prove that : (2A_1-A_2)(2A_2-A_1) =ab .

If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c respectively, prove that, (a)/(x) + (c )/(y) = 2

If A_(1) and A_(2) are two A.M.'s between a and b, prove that (i) (2A_(1)-A_(2))(2A_(2)-A_(1))=ab (ii) A_(1)+A_(2)=a+b

If A_1 and A_2 are two A.M.’s between a and b, prove that : A_1+A_2 =a+b .