Solve equation for real solution x^3-1=0
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Luca B.
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calendarEducator since 2011
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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.
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atyourservice | Student
x^3-1=0
+1 +1
x^3 =1
and the answer is 1 because cube root of 1 is 1
1x1x1= 1
ainsleyharris | Student
work backwards, 0+1 =1. therefore, x^3 has to equal 1, meaning that x is 1.
1^3=1. 1-1=0.
baracuda123 | Student
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
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