If a2 , b2 , c2 are in ap prove that a/b+c , b/c+a , c/a+b are also in ap

[Dhanalakshmi]

If a² , b² , c² are in ap prove that a/b+c , b/c+a , c/a+b are also in ap and 1/b+c , 1/c+a, 1/a+b are also in ap

[Dhanalakshmi]

Let us consider the three terms :

Difference between 2^nd and first term is worked out as follows

Now we see the terms,

difference between second and first term is worked out as follows

from (5) and (6), we say that

are in A.P