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Question
Dear Ms Yang,

I was wondering if you could help solve an argument.  The equation is x^3 - y^3 = 5803.  I got an answer of x = 20, y = 13 and x = -13, y = -20.  My friend says to solve this, just set y^3 = 0 and then the answer is y = 0, x = cube root 5803.  There seems to be something wrong with his answer, but I can't show mathematically if he's right or wrong and why.  Would you be able to help clarify things?

Sincerely,

Alex D

Answer
You and your friend found three solutions, and they are correct. They are not, however, the only solutions.
Since there are two variables but only one equation, there are an infinite number of solutions.

Rearrange to solve for y:
y = x - 5803
y = ∛(x - 5803)
You can see that the domain is the set of real numbers.

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Janet Yang

Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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