Question

54x²+6(x²-9x+81)=-7-4x+x³​

Answer 1

Ответ:

60x^2=-493-58x+x^3

Объяснение:

54x^2+6(x^2-9x+81)=-7-4x+x^3=54x^2+(6x^2-54x+486)=-7-4x+x^3

54x^2+(6x^2-54x+486)=-7-4x+x^3=60x^2+-54x+486=-7-4x+x^3

60x^2+-54x+486=-7-4x+x^3 это 60x^2=-493-58x+x^3

Answer 2

To solve the equation 54x² + 6(x² - 9x + 81) = -7 - 4x + x³, you can follow these steps:

1. First, distribute the 6 on the left side of the equation:

   54x² + 6x² - 54x + 486 = -7 - 4x + x³

2. Combine like terms on both sides of the equation:

   60x² - 54x + 486 = -7 - 4x + x³

3. Move all terms to one side of the equation to set it to zero:

   60x² - 54x + 486 + 7 + 4x - x³ = 0

4. Rearrange the terms:

   -x³ + 60x² - 50x + 493 = 0

5. Now, this is a cubic equation. To solve it, you can try factoring or use numerical methods to find the roots. Factoring is not straightforward for cubic equations, so let's use numerical methods.

   One common numerical method for finding approximate solutions to cubic equations is the Newton-Raphson method. We'll start with an initial guess for a solution and iterate until we get a good approximation.

   Let's start with an initial guess of x = 1:

   -1³ + 60(1)² - 50(1) + 493 = -1 + 60 - 50 + 493 = 502

   Now, apply the Newton-Raphson formula to refine the solution:

   x₁ = x₀ - f(x₀) / f'(x₀)

   We'll need to find the derivative f'(x):

   f(x) = -x³ + 60x² - 50x + 493 f'(x) = -3x² + 120x - 50

   Now, plug in x₀ = 1 into the formula:

   x₁ = 1 - (502) / (-3(1)² + 120(1) - 50)

   Calculate x₁:

   x₁ ≈ 1 - (502) / (-3 + 120 - 50) ≈ 1 - (502) / 67 ≈ 1 - 7.49 ≈ -6.49

   Now, continue this process with x₁ as the new guess:

   x₂ = x₁ - f(x₁) / f'(x₁)

   x₂ ≈ -6.49 - [-(6.49)³ + 60(6.49)² - 50(6.49) + 493] / [-3(6.49)² + 120(6.49) - 50]

   Keep iterating until you converge to a solution. You can use a calculator or a numerical computing tool to perform these calculations iteratively. The exact solutions to cubic equations can be quite complex, so numerical methods are often used to approximate them.