Non-negative real number proofs

  • Thread starter Thread starter sara_87
  • Start date Start date
  • Tags Tags
    Proofs
sara_87
Messages
748
Reaction score
0
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 don't know how to start any of them. any hints would be v much appreciated.
 
Physics news on Phys.org


for 1: are you sure you don't mean

<br /> xy \le \frac{(x+y)^2}2<br />

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?
 


thanx for 1 and 2
for 3) i can't fill in the blank??
 


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
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top