# Solve equation for real solution x^3-1=0

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You need to remember the formula of the difference of two perfect cubes:

`a^3-b^3 = (a-b)(a^2+ab+b^2)`

Comparing the difference of two cubes to the given equation yields:

`x^3-1 = (x-1)(x^2 + x + 1)`

You need to solve for x the product `(x-1)(x^2 + x + 1)` = 0.

x - 1 = 0 => x = 1

Notice that `x^2 + x + 1` > 0 `AA` x `in` R

**The real solution to the given equation is x = 1.**

or...

x^3-1=0

you just add 1 to both sides

x^3= 1

then you know the cube root of 1 is just 1

x^3-1=0

+1 +1

x^3 =1

and the answer is 1 because cube root of 1 is 1

1x1x1= 1

work backwards, 0+1 =1. therefore, x^3 has to equal 1, meaning that x is 1.

1^3=1. 1-1=0.