Question

решите уравнение (х²+2х+2)(х²+2х-4)=-5 помогите пожалуйста и опишите подробно​

Answer 1

(х² + 2х + 2)(х² + 2х - 4)= -5

1 способ:

Пусть t = х² + 2х + 2

(х² + 2х + 2)(х² + 2х + 2 - 6)= -5

t (t - 6) = -5

t² - 6t = -5

t² - 6t + 5 = 0

D = b² - 4ac = 36 - 4 · 1 · 5 = 16

$x_{1} = \frac{-b + \sqrt{D}}{2a} = \frac{6+4}{2} = 3 + 2 = 5$

$x_{2} = \frac{-b - \sqrt{D}}{2a} = \frac{6-4}{2} = 3 - 2 = 1$

х² + 2х + 2 = 5

х² + 2х -3 = 0

D = b² - 4ac = 4 - 4 · 1 · (-3) = 16

$x_{1} = \frac{-b + \sqrt{D}}{2a} = \frac{-2+4}{2} = -1 + 2 = 1$

$x_{2} = \frac{-b - \sqrt{D}}{2a} = \frac{-2-4}{2} = -1 - 2 = -3$

х² + 2х + 2 = 1

х² + 2х + 1 = 0

D = b² - 4ac = 4 - 4 · 1 · 1 = 0

$x = -\frac{b}{2a} = \frac{-2}{2} = -1$

Ответ: -3; -1; 1.

2 способ:

Пусть t = х² + 2х - 4

(х² + 2х - 4 + 6)(х² + 2х - 4) = -5

(t + 6)t = -5

t² - 6t = -5

t² - 6t + 5 = 0

D = b² - 4ac = 36 - 4 · 1 · 5 = 16

$x_{1} = \frac{-b + \sqrt{D}}{2a} = \frac{6+4}{2} = 3 + 2 = 5$

$x_{2} = \frac{-b - \sqrt{D}}{2a} = \frac{6-4}{2} = 3 - 2 = 1$

х² + 2х + 2 = 5

х² + 2х -3 = 0

D = b² - 4ac = 4 - 4 · 1 · (-3) = 16

$x_{1} = \frac{-b + \sqrt{D}}{2a} = \frac{-2+4}{2} = -1 + 2 = 1$

$x_{2} = \frac{-b - \sqrt{D}}{2a} = \frac{-2-4}{2} = -1 - 2 = -3$

х² + 2х + 2 = 1

х² + 2х + 1 = 0

D = b² - 4ac = 4 - 4 · 1 · 1 = 0

$x = -\frac{b}{2a} = \frac{-2}{2} = -1$

Ответ: -3; -1; 1.