If `a ,b ,a n dc` are in A.P. `p ,q ,a n dr` are in H.P., and `a p ,b q ,a n dc r` are in G.P., then `p/r+r/p` is equal to `a/c-c/a` b. `a/c+c/a` c. `b/q+q/b` d. `b/q-q/b`

Options

A. `a/c-c/a`
B. `a/c+c/a`
C. `b/q+q/b`
D. `b/q-q/b`

Answer

B

Explanation

`p/r+r/p=(p^(2)+r^(2))/(pr)=((p+r)^(2)-2pr)/(pr)`
`=((4p^(2)r^(2))/q^(2)-2pr)/(pr)[{:(because" p,q,r are in H.P."),(" "thereforeq=(2pr)/(p+r)):}]`
`=(4pr)/q^(2)-2=(4b^(2))/(ac)-2`
`[because` ap,bq,cr are in A.P. `rArrb^(2)q^(2)=acpr]`
`=((a+c)^(2))/(ac)-2[a,b,c` are in A.P`rArr2b=a+c]`
`=a/c+c/a`