P+q+r=1 and pq+pr+qr=-1 and pqr= -1 find P^3+q^3+r^3
Answers
Answered by
2
(p+q+r)^3=p^3+q^3+r^3+(p+q+r)(pq+qr+rp)
by this identity
p^3+q^3+r^3=(p+q+r)^3-(p+q+r)(pq+qr+rp)
p^3+q^3+r^3=(1)^3-(1)(-1)
p^3+q^3+r^3=1-1
therefore p^3+q^3r^3=0
by this identity
p^3+q^3+r^3=(p+q+r)^3-(p+q+r)(pq+qr+rp)
p^3+q^3+r^3=(1)^3-(1)(-1)
p^3+q^3+r^3=1-1
therefore p^3+q^3r^3=0
Similar questions