If p+q+r = 1 and pq+qr+pr= -1 and pqr = -1. Find the value of p cube + q cube +r cube?

Question

If p+q+r = 1 and pq+qr+pr= -1 and pqr = -1 Find the
value of p cube + q cube +r cube?

Lovina Kansal · Accepted Answer

Dear student,

p+q+r=1 , pq+qr+rp=-1 , pqr=-1Now we know ,      p+q+r2=p2+q2+r2+2pq+qr+rp⇒12=p2+q2+r2+2-1⇒p2+q2+r2=3Now we also know that      p3+q3+r3-3pqr=p+q+rp2+q2+r2-pq-qr-rp⇒p3+q3+r3-3-1=13--1⇒p3+q3+r3=1

Regards