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Non-negative real number proofs

  1. Oct 5, 2008 #1
    1) proe that for all non-negative real numbers x and y:

    2) prove that the sum of 2 prime numbers strictly greater than 2 is even

    3) If n is a multiple of 3 then either n is odd or it is a multiple of six.

    I dont know how to start any of them. any hints would be v much appreciated.
  2. jcsd
  3. Oct 5, 2008 #2


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    Re: proofs

    for 1: are you sure you don't mean

    xy \le \frac{(x+y)^2}2

    Expand the right side here and see what you find.

    for 2: (same hint, two different wordings): What property does every prime number larger than 2 have?
    What makes 2 different from every other prime number?

    for 3: Any multiple of 3 is either odd or *****? (fill in the blank). if it is *****, what other number is the number a multiple of?
  4. Oct 5, 2008 #3
    Re: proofs

    thanx for 1 and 2
    for 3) i cant fill in the blank??
  5. Oct 5, 2008 #4


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    Re: proofs

    Write out a few multiples of 3 (six of them should be enough) - just make sure you pick some that are not odd integers.
    you may go "doh" when you see what the multiples that are not odd have in common
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