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Help with proof

  1. Jan 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove these propositions

    2. Relevant equations
    If x is rational, then x + sqrt(2) is irrational.
    If x + sqrt(2) is irrational, then x is rational.
    If xsqrt(2) is irrational, then x is rational.

    3. The attempt at a solution
    I've tried a couple of ways, but I always end up at a dead end. usually, I end up assuming what I need to prove.
  2. jcsd
  3. Jan 29, 2009 #2


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    The first proposition is true. The others aren't. Can you find a counterexample for them? As to proving the first can you show us what you tried?
  4. Jan 29, 2009 #3
    After working with it some more, I've gotten all but the last. Is a counter example something like e(sqrt(2))? But I don't know if that is rational or not.
  5. Jan 29, 2009 #4


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    That's too hard. In fact, I'm not sure anybody knows the answer to that. How about sqrt(3)*sqrt(2)?
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