Question

(x-4) (x ² + 15x +50)(x-2) =18x²​

Answer 1

    Решение : //////////////////////////////////////////////////

Answer 2

Let's solve the given equation step-by-step:

Given equation: (x - 4)(x² + 15x + 50)(x - 2) = 18x²

First, let's expand the expression on the left-hand side:

(x - 4)(x² + 15x + 50)(x - 2)

To do this, we'll use the distributive property of multiplication. We'll start by multiplying the first two binomials, and then we'll multiply the result with the third binomial:

(x - 4)(x² + 15x + 50)(x - 2) = (x² + 15x + 50)(x - 2) [Expand the first two binomials] = x²(x - 2) + 15x(x - 2) + 50(x - 2) [Use distributive property] = x³ - 2x² + 15x² - 30x + 50x - 100 [Multiply each term]

Now, we have:

x³ - 2x² + 15x² - 30x + 50x - 100 = 18x²

Next, combine like terms:

x³ + (15x² - 2x²) + (50x - 30x) - 100 = 18x²

Simplify further:

x³ + 13x² + 20x - 100 = 18x²

Now, move all the terms to one side of the equation to set it equal to zero:

x³ + 13x² + 20x - 100 - 18x² = 0

Combine the x² terms:

x³ - 5x² + 20x - 100 = 0

The equation is now in the form of a cubic equation (a third-degree polynomial). To solve for x, you could use various methods like factoring, synthetic division, or numerical methods. However, for this particular equation, factoring might not be straightforward, so you might need to use numerical methods to approximate the solutions.

Please note that without further information, it's not possible to determine the exact solutions of the cubic equation. If you have specific values of x for which the equation is satisfied, you can check if the equation holds true. Alternatively, if there was a mistake in the initial equation or if additional information is provided, the solution approach might change.