Question

If a, b, c are in A.P., prove that
1/√b+√c, 1/√c+√a, 1/√a+√b are in A.P.

Answer 1

Answer:

Let

1/b+c, 1/c+a, 1/a+b

multiply (a+b+c)

then

1+a/b+c, 1+b/c+a, 1+c/a+b

add -1 in series

now

a/b+c, b/c+a, c/a+b

again multiply (a+b+c)

now

a + a^2/b+c, b + b^2/a+c , c + c^2/a+b

now add -(ab+ac)

you get

a^2 , b^2 , c^2