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Math Help - Prove there are no rational solutions

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    Prove there are no rational solutions

    Prove that there are no rational solutions to the equation x^3 + x^2 = 1
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    Quote Originally Posted by treetheta View Post
    Prove that there are no rational solutions to the equation x^3 + x^2 = 1
    Let x=\frac{p}{q} with p\wedge q=1; you get p^3+qp^2=q^3 hence (...) q|p and thus q=1, which mean x is an integer. I let you fill in the (quick) dots and handle it from there (beware, x^3 may be negative).
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by treetheta View Post
    Prove that there are no rational solutions to the equation x^3 + x^2 = 1
    Or, maybe the rational root theorem...
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