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Homework Help: Proof by contradiction

  1. Jun 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove or disprove the statement:
    13 + 2√6 is an irrational number
    Given that √6 is irrational


    2. Relevant equations

    Rational number = p/q where p and q are integers

    3. The attempt at a solution
    Assume that 13 + 2√6 is a rational number
    Rational number = p/q where p and q are integers
    Let 13 = n where n is an integer
    Let 2√6 = x
    x + n = p/q
    x = ( p/q) – n
    x = (p – qn)/q
    We have shown that x can be expressed as a ratio of two integers. This is a contradiction because we know that x is irrational. Therefore, the statement: 13 + 2√6 is an irrational number is proven true.
     
  2. jcsd
  3. Jun 12, 2010 #2
    Correct idea, but x = 2√6, and you are given that √6 is irrational.
     
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