Question

If b², a², c² are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______

Options

• A.P.

• G.P.

• A.P. and G.P.

• None of these

Answer 1

If b², a², c² are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in A.P.

Explanation:

Given that b², a², c² are in A.P.

∴ a² – b² = c² – a²

`\implies` (a – b) (a + b) = (c – a) (c + a)

`\implies 1/(b + c) = 1/(a + b) = 1/(c + a) - 1/(b + c)`

`\implies 1/(a + b), 1/(b + c), 1/(c + a)` are in A.P.