Question

If $a^2,b^2,c^2$are in A.P., then ${(b+c)}^{-1},{(c+a)}^{-1}$and ${(a+b)}^{-1}$will be in?

• A. H.P.
• B. G.P.
• C. A.P.
• D. None of these

Answer 1

The correct option is C

A.P.

Explanation for the correct option:

To find the correct relation:

Given $a^2,b^2,c^2$are in A.P.

Add $ab+ac+bc$ to each term, we get

$a^2+ab+ac+bc,b^2+ab+ac+bc,c^2+ab+ac+bc$ are in A.P.

$(a+b)(a+c),(b+c)(b+a),(c+a)(c+b)$are in A.P.

Divide each term by $(a+b)(b+c)(c+a)$

$\frac{1}{(b+c)},\frac{1}{(c+a)},\frac{1}{(a+b)}$are in A.P.

So, ${(b+c)}^{-1},{(c+a)}^{-1},{(a+b)}^{-1}$in A.P.

Hence, the correct option is C.