Решение
(x² + 4x)(x² + 4x - 17) + 60 = 0
Пусть x² + 4x = y, тогда
y*(y - 17) + 60 = 0
y² - 17y + 60 = 0
D = 289 - 4*1*60 = 49
y₁ = (17 - 7)/2
y₁ = 5
y₂ = (17 + 7)/2
y₂ = 12
1) ² + 4x = 5
x² + 4x - 5 = 0
x₁ = - 5
x₂ = 1
2) x² + 4x = 12
x² + 4x - 12 = 0
x₃ = - 6
x₄ = 2
Ответ: x₁ = - 5; x₂ = 1; x₃ = -6; x₄ = 2
2) (x² - 5x)(x² - 5x + 10) + 24 = 0
Пусть x² - 5x = z тогда
z*(z + 10) + 24 = 0
z² + 10z + 24 = 0
z₁ = - 6
z₂ = - 4
1) x² - 5x = - 6
x² - 5x + 6 = 0
x₁ = 2
x₂ = 3
2) x² - 5x = - 4
x² - 5x + 4 = 0
x₃ = 1
x₄ = 4
Ответ:
x₁ = 2; x₂ = 3; x₃ = 1; x₄ = 4