If the equations of three concurrent lines are px+6y - 8 = 0, qx+5y - 8 = 0
and rx+4y - 8 = 0, then the value of p + r is
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Answer:
Accordingtoquestion−−−
given,linespx+qy+r=0,qx+ry+p=0andrx+py+q=0areconcurrent:
so,that−
∣
∣
∣
∣
∣
∣
∣
∣
pqr
qrp
rpq
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒p(qr−p
2
)−q(q
2
−pr)+r(pq−r
2
)=0
⇒pqr−p
3
−q
3
+pqr+pqr−r
3
=0
⇒3pqr−p
3
−q
3
−r
3
=0
∴p
3
+q
3
+r
3
=3pqr
sothatthecorrectoptionisC.
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