(x² - 5x)² + 10(x² - 5x + 1) + 14 = 0
Замена x² - 5x = t
t² + 10(t + 1) + 14 = 0
t² + 10t + 10 + 14 = 0
t² + 10t + 24 = 0
D₁ = 5² - 24 = 1 = 1² - упрощенный дискриминант
t₁ = 5 + 1 = 6
t₂ = 5 - 1 = 4
Совокупность уравнений:
[ x² - 5x = 6
[ x² - 5x = 4
[ x² - 5x - 6 = 0
[ x² - 5x - 4 = 0
1) x² - 5x - 6 = 0
D = 25 - 4 · 6 = 1 = 1²
x₁ = (5 + 1) / 2 = 3
x₂ = (5 - 1) / 2 = 2
2) x² - 5x - 4 = 0
D = 25 - 4 · 4 = 9 = 3²
x₁ = (5 + 3) / 2 = 4
x₂ = (5 - 3) / 2 = 1
Ответ: 1; 2; 3; 4