求满足x-1的3次立方根+1=x的值

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求满足x-1的3次立方根+1=x的值
求满足x-1的3次立方根+1=x的值

求满足x-1的3次立方根+1=x的值
(x-1)^(1/3)+1=x,原方程两边同时3次方得:x-1=(x-1)^3,化简得:x(x-1)(x-2)=0.
所以,解为:x1=0,x2=1,x3=2.

原式为(x-1)^(1/3) + 1 = x
(x-1)^(1/3) = x - 1
两边立方得:x - 1 = (x - 1)³
x - 1 = x³ - 3x² + 3x - 1
x³- 3x² + 2x² = 0
x(x - 3x +2)= 0
x(x-1)(x-2)= 0
x1 = 0;x2 = 1;x3 = 2;