Решите: x^3-6x^2+12x-8=0...если можно с объяснением :)
x³-6x²+12x-8=0
x³-8 - 6x²+12x=0
x³- 2³ - 6x²+12x=0
(x- 2)(х²+2х+4) - 6x(х -2)=0
(x- 2)(х²+2х+4-6х) =0
(x- 2)(х²-4х+4) = 0
(x- 2)(х²-4х+ 2²) = 0
(x- 2)(х -2)² = 0
(x- 2)³ = 0
х-2=0
х=2
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x³-6x²+12x-8=0
x³-8 - 6x²+12x=0
x³- 2³ - 6x²+12x=0
(x- 2)(х²+2х+4) - 6x(х -2)=0
(x- 2)(х²+2х+4-6х) =0
(x- 2)(х²-4х+4) = 0
(x- 2)(х²-4х+ 2²) = 0
(x- 2)(х -2)² = 0
(x- 2)³ = 0
х-2=0
х=2