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Algebraic Weapons · Challenge problem

Let rr, ss, tt be the roots of x3−4x+2=0x^3 - 4x + 2 = 0. What is (r2+r+1)(s2+s+1)(t2+t+1)(r^2 + r + 1)(s^2 + s + 1)(t^2 + t + 1)?