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guroten
Jan29-09, 05:59 PM
1. The problem statement, all variables and given/known data
Prove these propositions


2. Relevant equations
If x is rational, then x + sqrt(2) is irrational.
If x + sqrt(2) is irrational, then x is rational.
If xsqrt(2) is irrational, then x is rational.

3. The attempt at a solution
I've tried a couple of ways, but I always end up at a dead end. usually, I end up assuming what I need to prove.
Dick
Jan29-09, 06:08 PM
1. The problem statement, all variables and given/known data
Prove these propositions


2. Relevant equations
If x is rational, then x + sqrt(2) is irrational.
If x + sqrt(2) is irrational, then x is rational.
If xsqrt(2) is irrational, then x is rational.

3. The attempt at a solution
I've tried a couple of ways, but I always end up at a dead end. usually, I end up assuming what I need to prove.

The first proposition is true. The others aren't. Can you find a counterexample for them? As to proving the first can you show us what you tried?
guroten
Jan29-09, 06:38 PM
After working with it some more, I've gotten all but the last. Is a counter example something like e(sqrt(2))? But I don't know if that is rational or not.
Dick
Jan29-09, 09:08 PM
After working with it some more, I've gotten all but the last. Is a counter example something like e(sqrt(2))? But I don't know if that is rational or not.

That's too hard. In fact, I'm not sure anybody knows the answer to that. How about sqrt(3)*sqrt(2)?