(х + 1)⁴ + (х + 1)² - 6 = 0
((х + 1)²)² + (х + 1)² - 6 = 0
t = (x + 1)²
t² + t - 6 = 0
D = 1² - 4 · 1 · (-6) = 2 + 24 = 25; √25 = 5
t₁ = (-1 - 5)/2 = -3
t₂ = (-1 + 5)/2 = 2
(x + 1)² = -3
x² + 2x + 1 + 3 = 0
x² + 2x + 4 = 0
D = 2² - 4 · 1 · 4 = 4 - 16 = -12 < 0, решений нет
(x + 1)² = 2
х² + 2х + 1 - 2 = 0
х² + 2х - 1 = 0
D = 2² - 4 · 1 · (-1) = 4 + 4 = 8; √8 = 2√2
x₁ = (-2 + 2√2)/2 = -1 +√2
х₂ = (-2 - 2√2)/2 = -1 - √2