Question

(x+2)(x+1)x(x-1) = 24

Answer 1

(x+2)(x+1)x(x-1) = 24

x(x + 1) * (x+2)(x - 1) = 24

(x^2 + x) * (x^2 + 2x - x - 2) = 24

(x^2 + x)(x^2 + x - 2) = 24

x^2 + x = t

t*(t - 2) = 24

t^2 - 2t - 24 = 0

D = 4 + 96 = 100

t12 = (2 +- 10)/2 = 6  -4

1. t = -4

x^2 + x + 4 = 0

D = 1 - 12 = -11  < 0 действительных корней нет (комплексные х12 = (-1 +- i√11)/2 )

2. t = 6

x^2 + x - 6 = 0

D = 1 + 24 = 25

x12 = (-1 +- 5)/2 = -3  2

ответ действительные корни -3  и 2 (комплексные х12 = (-1 +- i√11)/2 )

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ну можно замену сделать

y = x + 0.5

тогда (y + 3/2)(y + 1/2)(y - 1/2)(y - 3/2) = 24

(y^2 - 1/2^2)(y^2 - (3/2)^2) = 24

z = y^2 - 1/4  итд

Answer 2

To solve the equation $(x+2)(x+1)x(x-1) = 24$, we can follow these steps:

1. Expand the left-hand side of the equation: $(x+2)(x+1)x(x-1) = x(x+1)x(x-1) + 2(x+1)x(x-1)$ $= x^2(x^2-1) + 2x(x^2-1)$ $= x^4 - x^2 + 2x^3 - 2x$

2. Combine like terms: $x^4 + 2x^3 - x^2 - 2x = 24$

3. Move all terms to one side of the equation: $x^4 + 2x^3 - x^2 - 2x - 24 = 0$

At this point, the equation is a quartic equation (a polynomial of degree 4), and finding its solutions analytically can be quite challenging. You might need to use numerical methods or a graphing calculator to approximate the solutions.