Question

(х+1)(х+2)(х+3)(х+4)=24 решить уравнение

Answer 1

Как то так в общем,......

Answer 2

To solve the equation (x+1)(x+2)(x+3)(x+4) = 24, we can first simplify the left-hand side by expanding the product:

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(x+1)(x+2)(x+3)(x+4) = (x^2+5x+4)(x^2+5x+6) 
                      = x^4 + 10x^3 + 35x^2 + 50x + 24

So the equation can be rewritten as:

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x^4 + 10x^3 + 35x^2 + 50x + 24 = 24

Simplifying further:

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x^4 + 10x^3 + 35x^2 + 50x = 0

Factoring out x:

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x(x^3 + 10x^2 + 35x + 50) = 0

The equation has two solutions: x = 0 and x satisfies the cubic equation x^3 + 10x^2 + 35x + 50 = 0.

The cubic equation can be solved by factoring it, or by using numerical methods such as Newton's method. However, the solutions are complex and not easy to compute by hand.

Therefore, the solutions to the original equation are x = 0 and the solutions of the cubic equation x^3 + 10x^2 + 35x + 50 = 0, which are complex.