х⁵ - х⁴ - 2х³ + 2х² + х - 1 = 0
х⁴(х-1) - 2х²(х-1) + (х-1) = 0
(х-1)(х⁴-2х²+1) = 0
х₁ = 1
х⁴-2х²+1 = 0
пусть х² = t, тогда
t²-2t+1 = 0
D = 4-4 = 0
t = 2/2 = 1
x₂ = 1
x₃ = -1
Сумма корней: х₁+х₂+х₃ = 1+1-1 = 1
х⁵ - х⁴ - 2х³ + 2х² + х - 1 = 0
х⁴(х-1) - 2х²(х-1) + (х-1) = 0
(х-1)(х⁴-2х²+1) = 0
х₁ = 1
х⁴-2х²+1 = 0
пусть х² = t, тогда
t²-2t+1 = 0
D = 4-4 = 0
t = 2/2 = 1
x₂ = 1
x₃ = -1
Сумма корней: х₁+х₂+х₃ = 1+1-1 = 1