Question

(X+1)(x+2)(x+3)(x+4)=(x+1)(X+2)(x+3)(x+5)

Answer 1

(x + 1)(x + 2)(x + 3)(x + 4) = (x + 1)(x + 2)(x + 3)(x + 5)

• Перенесём всё в левую часть:

(x + 1)(x + 2)(x + 3)(x + 4) - (x + 1)(x + 2)(x + 3)(x + 5) = 0

• Вынесем за скобки общие слагаемые:

(x + 1)(x + 2)(x + 3)((x + 4) - (x + 5)) = 0

• Раскроем скобки внутри:

(x + 1)(x + 2)(x + 3)(x + 4 - x - 5) = 0

• Упростим:

(x + 1)(x + 2)(x + 3) • (-1) = 0

-(x + 1)(x + 2)(x + 3) = 0

• Система:

{ -(x + 1) = 0

{ x + 2 = 0

{ x + 3 = 0

<=>

{ x₁ = -1

{ x₂ = -2

{ x₃ = -3

Ответ: x₁ = -1 ; x₂ = -2 ; x₃ = -3

Answer 2

To solve the given equation $(x+1)(x+2)(x+3)(x+4) = (x+1)(x+2)(x+3)(x+5)$, we can start by canceling out common factors on both sides of the equation:

$(x+1)(x+2)(x+3)(x+4) = (x+1)(x+2)(x+3)(x+5)$

We can divide both sides by $(x+1)(x+2)(x+3)$ to simplify the equation:

$x+4 = x+5$

Now, subtract $x$ from both sides:

$4 = 5$

Since $4$ is not equal to $5$, there are no values of $x$ that satisfy the given equation. The original equation is not valid.