If lines `p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0` are concurrent, then prove that `p+q+r=0(w h e r ep ,q ,r` are distinct`)dot`

Explanation

for concurrency of three lines
`px+qy+r=0 , qx+ ry+p =0,rx+py+q=0`
we must have `|{:(p,,q,,r),(q,,r,,p),(r,,p,,q):}|=0`
`" or " 3pqr -p^(3)-q^(3)-r^(3)=0`
`" or "(p+q+r)(p^(2)+q^(2)+r^(2)-pq-pr-rq)=0`
`" or " p+q+r=0`