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) .

Find the A.M. between : 6 and -8.

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_1 and A_2 are two A.M.’s between a and b, prove that : A_1+A_2 =a+b .

Prove that : B^(c) -A^(c)=A-B .

If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find the value of n.

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : a/x+c/y=2 .

Prove that : (A-B) nn (B-A)=phi .

If a,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : 1/x+1/y=2/b .