Is (x+sqrt(2)) or (-x+sqrt(2)) rational?

[mmd50]

Homework Statement

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

Homework Equations

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

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
x+sqrt{2} = \frac{p}{q} [\tex]<br /> <br /> 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!