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

Engineering

Mathematics

Introduction to Determinants

Question

p + q + r = 0

p³ + q³ + r³ = 3 pqr

p² + q² + r² – pq – qr – rp = 0

p² + q² + r² = 2(pq + qr + rp)

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$∣ \begin{array}{ccc} p & q & r \\ q & r & p \\ r & p & q \end{array} ∣ = 0$

p(rq – p²) – q(q² – rp) + r(qp – r²) = 0

3pqr – p³ – q³ – r³ = 0

p³ + q³ + r³ = 3pqr

p³ + q³ + r³ – 3pqr = 0

(p + q + r)(p² + q² + r² – pq – qr – pr) = 0

⇒ p + q + r = 0 or
p² + q² + r² – pq – qr – pr = 0

Please subscribe our Youtube channel to unlock this solution.