Question

if a^2,b^2,c^2 are in Ap, prove that a/b+c, b/c+a, c/a+b are in Ap

Answer 1

If a^2,b^2,c^2 are in ap
Then a,b,c will also be in ap
&its vice versa will also in ap
Then ,(a+b+c)/a ,a+b+c/b,a+b+c/c be in ap
Adding (-1) in each term
We find b+c/a,a+c/b,a+b/c will be in ap
Thus its vice versa ,a/b+c,b/c+a,c/a+b will be in ap
Proved