Solve algebraically x^3=x

Question

x³=x

Answer 1

Solve for zero to get

 

x³  - x = 0

 

factor out an x to get

 

x(x² - 1) = 0

 

Now factor what is in the parenthesis by using the difference of squares rule:

 

so

 

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

 

now solve for all three answers (separate the factors and set them ALL = 0)

 

x = 0  ,   x - 1 = 0  ,  x + 1 = 0

 

when you solve these three you get x = 0, x = 1, and x = -1

 

Bill Fanning

El Paso, TX