If `a/(b+c),b/(c+a),c/(a+b)` are in A.P. and `a+b+c!=0` prove that `1/(b+c),1/(c+a),1/(a+b)` are in A.P.

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

If (b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b) are in A.P. and a+b+c=0 then prove that a(b+c-a),b(c+a-b),c(a+b-c) are 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.

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

If (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P., then

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

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

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