# Where do I start

• Jun 11th 2006, 03:39 PM
Nichelle14
Where 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 PM
ThePerfectHacker
Quote:

Originally Posted by Nichelle14
If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.

Assume that,
$r+x$ is rational.
Thus,
$r+x=\frac{p}{q}$
Then,
$x=\frac{p}{q}-r$
But, $r$ is rational,
Thus,
$x$ must be rational.
----
Assume that,
$rx$ is rational.
Thus,
$rx=\frac{p}{q}$
Now, $r\not = 0$ thus,
$x=\frac{p}{rq}$
Thus, $x$ is rational.
• Jun 11th 2006, 04:40 PM
Nichelle14
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 PM
ThePerfectHacker
Quote:

Originally Posted by Nichelle14
Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.
Again thank you.

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