If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.

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- Jun 11th 2006, 03:39 PMNichelle14Where do I start
If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.

- Jun 11th 2006, 04:14 PMThePerfectHackerQuote:

Originally Posted by**Nichelle14**

is rational.

Thus,

Then,

But, is rational,

Thus,

must be rational.

A contradiction.

----

Assume that,

is rational.

Thus,

Now, thus,

Thus, is rational.

A contradiction. - Jun 11th 2006, 04:40 PMNichelle14
Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.

Again thank you. - Jun 11th 2006, 05:10 PMThePerfectHackerQuote:

Originally Posted by**Nichelle14**

Let us keep all you question in "Number Theory" section. I like to leave misselanous topic in that section.