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Math Help - Rational numbers problem

  1. #1
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    Rational numbers problem

    Which rational numbers t are such that
    3t^3+10t^2-3t
    is an integer?
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  2. #2
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    3t^3+10t^2-3t= t(3t^2+10t-3)

    Now solve the expression inside the brackets using the quadratic formula.

    Do you know this formula?
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  3. #3
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    Yes, I know this formula. I solved this problem few minutes ago. I will show my solution tomorrow. It is a little different from this above and not so simple.
    Maybe I am wrong.
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  4. #4
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    Here is my solution:

    It isn't so simple like this two posts above. Is it correct?
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Arczi1984 View Post
    Here is my solution:

    It isn't so simple like this two posts above. Is it correct?
    Why have you discounted the cases m=\pm 1

    CB
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  6. #6
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    In these two cases we should solve two simple equations like pickslides noted. So I omitted them in my solution.
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by Arczi1984 View Post
    In these two cases we should solve two simple equations like pickslides noted. So I omitted them in my solution.
    It would make things a bit clearer if you say something like, let t=n/m be a rational number such that 3t^3+10t^2-3t is an integer.

    Now the cases m=\pm 1 correspond to t being an integer, but 3t^3+10t^2-3t is an integer when ever t is an integer so all integer values of t are trivially among those which make the expression in question an integer.

    Or am I still misunderstanding something?

    CB
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  8. #8
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    Yes, You're right.
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