Question

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

• A. p.q.r are in A.P.
• B. P², q², r² are in A.P.
• C. 1/p, 1/q, 1/r are in A.P.
• D. None of these

Answer 1

The correct option is B

P², q², r² are in A.P.

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

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

⇒ $q^2$ - $p^2$ = $r^2$ - $q^2$ ⇒ $p^2$, $q^2$, $r^2$ are in A.P.