Найдите сумму корней уравнения

x^3 - 6x^2 + 6x = 1

X³-6x²+6x=1

x³-6x²+6x-1=0

(x³-1) - (6x²-6x) = 0

(x-1) (x²+x+1) - 6x (x-1) = 0

(x-1) (x²+x+1-6x) = 0

(x-1) (x²-5x+1) = 0

x-1=0 x²-5x+1=0

x₁=1 D = (-5) ²-4*1*1=25-4=21

x₂ = (5+√21) / 2; x₃ = (5-√21) / 2

x₁+x₂+x₃=1 + ((5+√21) / 2) + ((5-√21) / 2) = 1 + ((5+√21+5-√21) / 2) =

= 1 + (10/2) = 1+5 = 6

Ответ: 6