ThinkDifferent

OK! Now some algebra.

The real set {a, b, c} is such that the equation

x³ + ax² + bx + c = 0

has three distinct real roots and

(x² + x + 2005)³ + a(x² + x + 2005)² + b(x² + x + 2005) + c > 0

for all real values of x. Show that, for the same set {a, b, c},

(2005)³ + a(2005)² + b(2005) + c > 1/64