Question

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

Answer 1

(x²+4x)²+7x²+28x+12=0 
(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

Answer 2

(x²+4x)²+7x²+28x+12=0 

(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

Answer 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!