InterviewSolution
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InterviewSolution
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If lines `p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0`areconcurrent, then prove that `p+q+r=0(w h e r ep ,q ,r`are distinct`)dot`A. `p+q+r=0`B. `p^(2)+q^(2)+r^(2)=pq+qr+rp`C. `p^(3)+q^(3)+r^(3)=3pqr`D. none of these |
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Answer» Correct Answer - C The lines `px+qy+r=0, qx+ry+p=0` and `rx+py+q=0` are concurrent, if `|{:(p,q,r),(q,r,p),(r,p,q):}|=0` `implies (p+q+r)^(2)(p^(2)+q^(2)+r^(2)-pq-qr-rp)=0` `implies p^(3)+q^(3)+r^(3)-3pqr=0implies p^(3)+q^(3)=3pqr` |
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