Question

(x²+2)-8(x²+2)+12=0 срочно, пожалуйста решить с помощью ввебения новой переменной

Answer 1

(x² + 2) - 8(x² + 2) + 12 = 0
обозначим у = x² + 2, получим и решим уравнение
у² - 8у + 12 = 0
D =  (-8)² - 4 · 1 · 12 = 64 - 48 = 16; √16 = 4
у₁ = (8 - 4)/2 = 2
у₂ = (8 + 4)/2 = 6
теперь вспомним, что у = x² + 2 и решим уравнения
х² + 2 = 2                   и х² + 2 = 6
х² = 0                             х² = 4
х₁ = 0                             х₂ = 2, х₃ = -2
Ответ: -2; 0; 2.

Answer 2

Solving the Quadratic Equation using a New Variable

To solve the quadratic equation (x²+2)-8(x²+2)+12=0 with the help of a new variable, we can follow these steps:

1. Let's introduce a new variable, say u, to simplify the equation.

2. We can substitute u = (x²+2). This will allow us to rewrite the given equation in terms of u and then solve for u.

3. After solving for u, we can then substitute back (x²+2) for u to find the values of x.

Let's proceed with these steps.

Step 1: Introduce a New Variable

We introduce a new variable u such that u = (x²+2).

Step 2: Rewrite the Equation in Terms of u

Substituting u = (x²+2), the given equation becomes: (u) - 8(u) + 12 = 0

Step 3: Solve for u

Now, we can solve for u by simplifying the equation: (u) - 8(u) + 12 = 0 -7u + 12 = 0 -7u = -12 u = 12/7

Step 4: Substitute back to find x

Now that we have found the value of u, we can substitute back (x²+2) for u: (x²+2) = 12/7

Step 5: Solve for x

To solve for x, we can rearrange the equation: x² = 12/7 - 2 x² = 12/7 - 14/7 x² = -2/7

Step 6: Find the Values of x

Taking the square root of both sides, we get: x = ±√(-2/7)

So, the solutions for x are: x = √(-2/7) and x = -√(-2/7).

By introducing the new variable u and following these steps, we have solved the quadratic equation (x²+2)-8(x²+2)+12=0 and found the values of x.