Problem: If p,q and r are distinct roots of x3−x2+x−2=0, then p3+q3+r3 equals
Answer Choices:
A. −1
B. 1
C. 3
D. 5
E. none of these
Solution:
Substituting the identity
p2+q2+r2=(p+q+r)2−2(pq+qr+rp)
into the identity
p3+q3+r3=(p+q+r)(p2+q2+r2−pq−qr−rp)+3pqr
yields
p3+q3+r3=(p+q+r)[(p+q+r)2−3(pq+qr+rp)]+3pqr=1[12−3(1)]+3(2)=4