if `a, b, c` are in `H. P.,` prove that `(1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2`

If a,b,c be in H.P prove that (1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2

If a,b,c are in A.P. prove that: a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P.

Suppose a, b, c are in A.P.Prove that a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P.

If a,b,c are in A.P.prove that: a((1)/(b)+(1)/(c)),b((1)/(c)+(1)/(a)),c((1)/(a)+(1)/(b)) are in A.P.

If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is also in A.P.

If a,b,c are in H.P., then the value of ((1)/(b)+(1)/(c)-(1)/(a))((1)/(c)+(1)/(a)-(1)/(b)) is

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If (b-c)^(2) , (c-a)^(2), (a-b)^(2) are in A.P. then prove that (1)/(b-c) , (1)/(c-a), (1)/(a-b) are also in A.P.