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Irrational Proof

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that for each real number x, (x+sqrt(2)) is irrational or (-x+sqrt(2)) is irrational.


    2. Relevant equations

    We have already proven sqrt(2) is irrational
    and a rational+an irrational=irrational.


    3. The attempt at a solution

    Proof by contradiction.

    Assume (x+sqrt(2)) or (-x+sqrt(2)) is rational.

    First set (x+sqrt(2))=(m/n) for some integers m and n.

    I get stuck here at where to go with the contradiction.
     
  2. jcsd
  3. Sep 30, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    so say the positive sum is rational
    [tex]x+sqrt{2} = \frac{p}{q} [\tex]

    then what is x? try using it to substitute into the negative sum
     
  4. Sep 30, 2009 #3
    x=sqrt(2)

    so...

    2(sqrt(2))=(m/n)

    I think I can take it from here. Thanks!!
     
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