Question

(х+1)³+(х-1)³-2х³=12​

Answer 1

Ответ:

x = 2

Объяснение:

x³ + 3x² + 3x + 1 + x³ - 3x² + 3x - 1 - 2x³ =12

6x = 12

x = 12/6

x = 2

Answer 2

To solve the equation (x+1)³ + (x-1)³ - 2x³ = 12, we can start by expanding the cubes and simplifying the equation.

Expanding (x+1)³, we get: (x+1)³ = x³ + 3x² + 3x + 1

Expanding (x-1)³, we get: (x-1)³ = x³ - 3x² + 3x - 1

Substituting these values back into the equation, we have: (x³ + 3x² + 3x + 1) + (x³ - 3x² + 3x - 1) - 2x³ = 12

Simplifying further, we combine like terms: x³ + x³ + 3x² - 3x² + 3x + 3x - 2x³ + 1 - 1 = 12

Combining like terms, we have: 2x³ + 6x = 12

Divide both sides of the equation by 2 to isolate the cubic term: x³ + 3x = 6

Now, we can solve this cubic equation. Unfortunately, there is no general formula for solving cubic equations, but we can use numerical methods or approximate the solutions. One possible method is the Newton-Raphson method, which involves making an initial guess and iterating to converge on the solution.

Let's use an initial guess of x = 1: x₀ = 1

Using the Newton-Raphson method, the iterative formula is: xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ)

where f(x) = x³ + 3x - 6 and f'(x) is the derivative of f(x).

Let's calculate the solution using the Newton-Raphson method:

1. Calculate f(x₀): f(1) = 1³ + 3(1) - 6 = -2

2. Calculate f'(x₀): f'(1) = 3(1)² + 3 = 6

3. Calculate x₁: x₁ = x₀ - f(x₀)/f'(x₀) = 1 - (-2)/6 = 1 + 2/6 = 1 + 1/3 = 4/3

4. Repeat steps 1-3 until convergence.

Using the Newton-Raphson method, we can approximate the solution of the equation (x+1)³ + (x-1)³ - 2x³ = 12 to be x ≈ 4/3 or approximately 1.3333.