# Non-negative real number proofs

1. Oct 5, 2008

### sara_87

1) proe that for all non-negative real numbers x and y:
xy(<or=)((x+y)/2)^2

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. Oct 5, 2008

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?

3. Oct 5, 2008

### sara_87

Re: proofs

thanx for 1 and 2
for 3) i cant fill in the blank??

4. Oct 5, 2008

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