Cubic Roots
Source: AIME 2008II Problem 7
April 3, 2008
VietaAMCAIMEalgebrapolynomialAIME I
Problem Statement
Let , , and be the three roots of the equation
8x^3\plus{}1001x\plus{}2008\equal{}0.Find (r\plus{}s)^3\plus{}(s\plus{}t)^3\plus{}(t\plus{}r)^3.