Irrational Proof

mmd50

1. The problem statement, all variables and given/known data

Prove that for each real number x, (x+sqrt(2)) is irrational or (-x+sqrt(2)) is irrational.


2. Relevant equations

We have already proven sqrt(2) is irrational
and a rational+an irrational=irrational.


3. The attempt at a solution

Proof by contradiction.

Assume (x+sqrt(2)) or (-x+sqrt(2)) is rational.

First set (x+sqrt(2))=(m/n) for some integers m and n.

I get stuck here at where to go with the contradiction.

lanedance

so say the positive sum is rational
[tex]x+sqrt{2} = \frac{p}{q} [\tex]

then what is x? try using it to substitute into the negative sum

mmd50

x=sqrt(2)

so...

2(sqrt(2))=(m/n)

I think I can take it from here. Thanks!!