Question

( frac{1}{9+r}, frac{1}{r+p}, frac{1}{p+q}: A P )
( Rightarrow frac{1}{r+p}-frac{1}{q+r}=frac{1}{p+q}-frac{1}{r+p} )
( Rightarrow frac{q+r-r-p}{(r+p)(q+r)}=frac{r+p-p-q}{(p+q)(r+p)} )
( Rightarrow frac{q-p}{q+r}=frac{r-q}{p+q} )
( Rightarrow quad(q-p)(q+p)=(r-q)(r+q) )
( Rightarrow quad q^{2}-p^{2}=r^{2}-q^{2} )
( Rightarrow quad 2 q^{2}=p^{2}+sigma^{2} )
( Rightarrow p^{2}, q^{2}, r^{2} ) are in ( A P )
option ( (B) )

# 1 1 1 - are in A.P., then q+r'r+pp+q (A) p, q, r are in A.P. in 1 11 (C) --- are in A.P. (B) p, q, r2 are in A.P. (D) none of these par

Solution