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`.

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 .

If a,b,c are in G.P. and x,y are the arithmetic means of a,b and b,c respectively. Then prove that a/x+c/y=2 and 1/x+1/y=2/b .

If a, b, c are in G.P. and x, y are arithmetic mean of a, b and b, c respectively, then 1/x +1/y is equal to :

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

If a be the A.M. and x, y be the two G.M's between b and c, show that x^3+y^3=2abc .

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.

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

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then

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

If x,y,z are in G.P. and a^x= b^y=c^z , prove that log_b a. log_b c=1 .