Question

(x-1)(x^2-2x+6)-(x-3)(x^2+8)=18

Answer 1

(x - 1)(x² - 2x + 6) - (x - 3)(x² + 8) = 18

x³ - 2x² + 6x - x² + 2x - 6 - x³ - 8x + 3x² + 24 = 18

18 = 18

Ответ : x ∈ R

Answer 2

(x - 1)(x² - 2x + 6) - (x - 3)(x² + 8) = 18

x³ - 2x² + 6x - x² + 2x - 6 - x³ - 8x + 3x² + 24 = 18

18 = 18

Ответ : x ∈ R

Объяснение:вот так

Answer 3

Let's solve the equation:

(x - 1)(x^2 - 2x + 6) - (x - 3)(x^2 + 8) = 18

First, we'll expand the expressions on both sides of the equation:

(x - 1)(x^2 - 2x + 6) = (x^3 - 2x^2 + 6x) - (x - 3)(x^2 + 8) = (x^2 - 2x + 6x) - (x^3 - 3x^2 + 8x)

Now, distribute the terms on the right side:

x^2 - 2x + 6x = x^3 - 3x^2 + 8x

Combine like terms:

x^2 + 4x = x^3 - 3x^2 + 8x

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

x^3 - 3x^2 + 8x - (x^2 + 4x) = 0

x^3 - 3x^2 + 8x - x^2 - 4x = 0

Combine like terms:

x^3 - 4x^2 + 4x = 0

Now, factor out an x from each term:

x(x^2 - 4x + 4) = 0

Now, we have a quadratic factor inside the parentheses, which can be further factored:

x(x - 2)(x - 2) = 0

Now, set each factor equal to zero and solve for x:

1. x = 0
2. x - 2 = 0 x = 2

So, the solutions to the equation are x = 0 and x = 2.