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Math Help - Where do I start

  1. #1
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    Where do I start

    If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.
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  2. #2
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    Quote Originally Posted by Nichelle14
    If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.
    Assume that,
    r+x is rational.
    Thus,
    r+x=\frac{p}{q}
    Then,
    x=\frac{p}{q}-r
    But, r is rational,
    Thus,
    x must be rational.
    A contradiction.
    ----
    Assume that,
    rx is rational.
    Thus,
    rx=\frac{p}{q}
    Now, r\not = 0 thus,
    x=\frac{p}{rq}
    Thus, x is rational.
    A contradiction.
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  3. #3
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    Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.
    Again thank you.
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  4. #4
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    Quote Originally Posted by Nichelle14
    Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.
    Again thank you.
    You are welcome.
    Let us keep all you question in "Number Theory" section. I like to leave misselanous topic in that section.
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