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Three lines px + qy+r=0, qx + ry+ p = 0 ...

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

A

`p+q+r=0`

B

`p^(2)+q^(2)+r^(2)=pr+rq`

C

`p^(3)+q^(3)+r^(3)=3pqr`

D

None of these

Text Solution

Verified by Experts

Given lines `px+qy+r=0`, `qx+ry+p=0`
and `rx+py+q=0` are concurrent.
`:. |{:(p,q,r),(q,r,p),(r,p,q):}|=0`
Applying `R_(1) to R_(1)+R_(2)+R_(3)` and taking common from `R_(1)`
`(p+q+r)|{:(1,1,1),(q,r,p),(r,p,q):}|=0`
`implies(p+q+r)(p^(2)+q^(2)+r^(2)-pq-qr-pr)=0`
`implies p^(3)+q^(3)+r^(3)-3pqr=0`
Therefore, `(a)` and `(c )` are the answers.
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