Question

(x² + 6x)2 + 8 (x2 + 6x) = 9;​

Answer 1

${({x}^{2} + 6x)}^{2} + 8({x}^{2} + 6x) = 9 \\ {x}^{2} + 6x = t \\ {t}^{2} + 8t - 9 = 0 \\ t_{1} + t_{2} = - 8 \\ t_{1} \times t_{2} = - 9 \\ t_{1} = - 9 \: \: \: \: \: \: \: \: \: t_{2} = 1 \\ 1) \: {x}^{2} + 6x + 9 = 0 \\ x_{1} + x_{2} = - 6 \\ x_{1} \times x_{2} = 9 \\ x_{1.2} = - 3 \\ 2) {x}^{2} + 6x - 1 = 0 \\ D = {6}^{2} - 4 \times 1 \times ( - 1) = 40 \\ x_{3.4} = \frac{ - 6 \pm \sqrt{40} }{2} = - 3 \pm \sqrt{10}$

Answer 2

Ответ :
x₁ = -3
x₂ = -3 - √10
x₃ = -3 +√10


(x² + 6x)² + 8(x² + 6x) = 9

t = x² + 6x

t² + 8t = 9
t² + 8t - 9 = 0

{ t₁ + t₂ = -8
{ t₁ × t₂ = -9

t₁ = -9
t₂ = 1

x² + 6x = -9
x² + 6x + 9 = 0

Решаю методом выделения полного квадрата :

(x + 3)² = 0
x + 3 = 0
x₁ = -3


x² + 6x = 1
x² + 6x - 1 = 0

Решаю тем же методом, что и прошлое уравнение :

(x + 3)² - 10 = 0
(x + 3)² = 10

x₂ = -3 - √10
x₃ = -3 + √10