Question

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

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

Answer 1

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

$\frac{1}{q+r},\frac{1}{r+p},\frac{1}{p+q}$

$\frac{2}{r+p}=\frac{1}{q+r}+\frac{1}{p+q}$

$\frac{2}{r+p}=\frac{p+q+q+r}{(q+r)(p+q)}$

$(2q+2r)(p+q)=(p+2q+r)(r+p)$

$2pq+2q^2+2rp+2rq=$$pr+p^2+2qr+2qp+r^2+rp$

$2q^2=p^2+r^2$

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