Problem: If the solutions of the equation x2+px+q=0 are the cubes of the solutions of the equation x2+mx+n=0, then
Answer Choices:
A. p=m3+3mn
B. p=m3−3mn
C. p+q=m3
D. (nm)3=qp
E. none of these answers
Solution:
Let a and b be the solutions of x2+mx+n=0; then
−mn=a+b=ab−pq=a3+b3=a3b3.
Since
a3+b3=(a+b)3−3ab(a+b)
we obtain
−p=−m3+3mn