
(x²+4x)²+7x²+28x+12=0 Помогите решить уравнение !!!Срочно!Пожалуйста


Ответы на вопрос

(x²+4x)²+7(x²+4x)+12=0
замена (x²+4x) =t
t²+7t+12=0
D=49-48=1
t12=(-7+-1)/2=-3 -4
(x²+4x) =-3
x²+4x+3=0
D=16-12=4
x1=-1
x2=-3
(x²+4x) =-4
x²+4x+4=0
D=16-16=0
x=-2
ответ -2 -1 -3



(x²+4x)²+7(x²+4x)+12=0
Пусть (x²+4x) = y
y²+7y+12=0
y1 = -3 y2 = -4
1) x²+4x = -3
x²+4x+3 = 0
x=-1 x =-3
2) x²+4x = -4
x=-2
Ответ -1;-2;-3



Solving the Equation (x²+4x)²+7x²+28x+12=0
To solve the equation (x²+4x)²+7x²+28x+12=0, we can follow these steps:
Step 1: Expand the equation Step 2: Simplify the equation Step 3: Solve the resulting quadratic equation
Let's go through each step in detail.
Step 1: Expand the Equation
The equation we have is (x²+4x)²+7x²+28x+12=0. To solve it, we need to expand the squared term (x²+4x)².
Expanding (x²+4x)², we get: (x²+4x)² = (x²+4x)(x²+4x) = x²(x²+4x) + 4x(x²+4x) = x⁴ + 4x³ + 4x³ + 16x² = x⁴ + 8x³ + 16x²
Now, our equation becomes: x⁴ + 8x³ + 16x² + 7x² + 28x + 12 = 0
Step 2: Simplify the Equation
Next, we simplify the equation by combining like terms. We add the terms with the same exponent.
x⁴ + 8x³ + 16x² + 7x² + 28x + 12 = 0
Combining the x² terms, we get: x⁴ + 8x³ + (16x² + 7x²) + 28x + 12 = 0 x⁴ + 8x³ + 23x² + 28x + 12 = 0
Step 3: Solve the Resulting Quadratic Equation
Now that we have a simplified equation, we can solve it by factoring or using the quadratic formula. In this case, we will use factoring.
x⁴ + 8x³ + 23x² + 28x + 12 = 0
To factor the equation, we look for common factors among the terms. In this case, we can see that (x + 1) is a factor.
(x + 1)(x³ + 7x² + 16x + 12) = 0
Now, we need to solve the remaining cubic equation x³ + 7x² + 16x + 12 = 0.
Unfortunately, finding the exact solutions for a cubic equation can be complex. However, we can use numerical methods or calculators to approximate the solutions.
I apologize for not being able to provide the exact solutions. If you have access to a graphing calculator or a numerical solver, you can input the equation x³ + 7x² + 16x + 12 = 0 to find the approximate solutions.
I hope this explanation helps you understand the process of solving the equation. If you have any further questions, feel free to ask!


Топ вопросов за вчера в категории Математика
Последние заданные вопросы в категории Математика
-
Математика
-
Литература
-
Алгебра
-
Русский язык
-
Геометрия
-
Английский язык
-
Химия
-
Физика
-
Биология
-
Другие предметы
-
История
-
Обществознание
-
Окружающий мир
-
География
-
Українська мова
-
Информатика
-
Українська література
-
Қазақ тiлi
-
Экономика
-
Музыка
-
Право
-
Беларуская мова
-
Французский язык
-
Немецкий язык
-
МХК
-
ОБЖ
-
Психология
-
Физкультура и спорт
-
Астрономия
-
Кыргыз тили
-
Оʻzbek tili