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Expert: Steve Holleran - 4/6/2007


Question
probly easy, but I'm getting confused....
x^3-1=0


Answer
Hi Ryan,

Yes, you're right--it is easy, BUT only if you know the factoring pattern.

Factoring  a difference of cubes goes like this:

A^3 - B^3 = (A - B)(A^2 + AB + B^2)

So, your example would be :

x^3 - 1 = 0

(x - 1)(x^2 + x + 1) = 0

And the only real solution is x = 1.  The other factor,
x^2 + x + 1 will not have real roots, only imaginary ones.
If you need to find them, use the quadratic formula on this factor.

You should get :  [-1 +/- i * sqrt(3)] / 2 .

If you need an explanation on that, let me know.

Steve Holleran

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Steve Holleran

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I can help with all math questions from basic math to Calculus. Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.

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33 years teaching experience in NJ public schools

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B.S. Mathematics : Wake Forest University 1972 M.S. Mathematics : Monmouth University 1981

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