Question

X^3-3x^2-9x-5=0 ...........

Answer 1

Ответ на фото , удачи , если что-то не понятно , спрашуй !)

Answer 2

To solve the equation x^3 - 3x^2 - 9x - 5 = 0, we can use various methods such as factoring, numerical methods, or finding approximate solutions. In this case, we will use a numerical method called the Newton-Raphson method to find an approximate solution.

The Newton-Raphson method requires an initial guess for the solution, and it iteratively refines the guess to get closer to the actual solution. Here's how it works:

1. Choose an initial guess for the root, let's say x0.
2. Use the formula: x1 = x0 - f(x0) / f'(x0), where f(x) is the given equation, and f'(x) is the derivative of f(x).
3. Repeat the process with x1 as the new guess until the difference between consecutive iterations is small enough.

Let's proceed with the calculations:

Given equation: f(x) = x^3 - 3x^2 - 9x - 5

Step 1: Choose an initial guess, let's say x0 = 2.

Step 2: Calculate f(x0) and f'(x0). f(x0) = 2^3 - 32^2 - 92 - 5 = 8 - 12 - 18 - 5 = -27 f'(x0) = 3x^2 - 6x - 9 f'(2) = 32^2 - 62 - 9 = 12 - 12 - 9 = -9

Step 3: Update the guess using the Newton-Raphson formula: x1 = x0 - f(x0) / f'(x0) x1 = 2 - (-27) / (-9) = 2 + 3 = 5

Now, the new guess is x1 = 5.

Step 4: Repeat the process with x1 as the new guess.

Step 5: Calculate f(x1) and f'(x1). f(x1) = 5^3 - 35^2 - 95 - 5 = 125 - 75 - 45 - 5 = 0 f'(x1) = -9 (same as before)

Since f(x1) is zero, it means that x1 is a root of the equation.

Therefore, one of the approximate solutions to the equation x^3 - 3x^2 - 9x - 5 = 0 is x ≈ 5.

Keep in mind that this method may converge to different roots depending on the initial guess. There may be additional real or complex roots to the equation that may require other methods to be found.