Question

If $\frac{1}{p+q},\frac{1}{q+r},\frac{1}{r+p}$ are in A.P. then

• A. p, q, r are in A.P.
• B. $q^2,p^2,r^2$ are in A.P.
• C. $p^2,q^2,r^2$ are in A.P.
• D. q, p, r are in A.P.

Answer 1

The correct option is B $q^2,p^2,r^2$ are in A.P.

$\frac{1}{q+r}-\frac{1}{p+q}=\frac{1}{r+p}-\frac{1}{q+r}$

$p^2-r^2=q^2-p^2\Rightarrow 2p^2=r^2+q^2$
$\therefore q^2,p^2,r^2$ are in A.P.