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# Advanced Math/x^3 - y^3 = 5803

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

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:
y³ = x³ - 5803
y = ∛(x³ - 5803)
You can see that the domain is the set of real numbers.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you very much. I was stuck on finding integer solutions, but nothing in the equation specifically demands an integer solution.

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#### Janet Yang

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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.

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

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