(х+1)^(1/3)+(х+2)^(1/3)+(х+3)^(1/3)=0 Как решать ответ подобрал, х=-2, а как разъяснить

Уравнение (х + 1)^(1/3) + (х + 2)^(1/3) + (х + 3)^(1/3) = 0 равносильно:

(х + 1)^(1/3) = -((х + 2)^(1/3) + (х + 3)^(1/3)).

Отсюда:

x + 1 = -((х + 2) + 3 * (х + 2)^(2/3) * (x + 3)^(1/3) + 3 * (х + 2)^(1/3) * (x + 3)^(2/3) + (x + 3)),

3x + 6 = -3 * ((х + 2)^(2/3) * (x + 3)^(1/3) + (х + 2)^(1/3) * (x + 3)^(2/3)),

(x + 2) + (х + 2)^(2/3) * (x + 3)^(1/3) + (х + 2)^(1/3) * (x + 3)^(2/3) = 0.

(x + 2)^(1/3) * ((x + 2)^(2/3) + (х + 2)^(1/3) * (x + 3)^(1/3) + (x + 3)^(2/3)) = 0.

Отсюда: (x + 2)^(1/3) = 0. То есть x + 2 = 0, что равносильно x = -2.

Или: (x + 2)^(2/3) + (х + 2)^(1/3) * (x + 3)^(1/3) + (x + 3)^(2/3) = 0.

[(x + 2)^(2/3) + (х + 2)^(1/3) * (x + 3)^(1/3) + (x + 3)^(2/3)] * [(х + 2)^(1/3) - (х + 3)^(1/3)] = 0, где (х + 2)^(1/3) - (х + 3)^(1/3)