Thread: Proving Inequalities

I needed to type the questions again because there was a typing mistake this morning when I originally posted the math questions.

QUESTION 1:

If a > 0, show that the solution set of the inequality x^2 < a consists of all numbers x for which -(sqrt{a}) < x < (sqrt{a}).

QUESTION 2:

If a > 0, show that the solution set of the inequality x^2 > a consists of all numbers x for which x > (sqrt{a}) OR x < -(sqrt{a}).

I hope this makes sense now.

Thanks.

Originally Posted by symmetry

QUESTION 2:

If a > 0, show that the solution set of the inequality x^2 > a consists of all numbers x for which x > (sqrt{a}) OR x < -(sqrt{a}).

Both ImPerfectHacker and CaptainBlack did this one in the other thread
as far as I can recall, and the other is a direct consequence of this result.

RonL

So, basically there is no need to go over the second part of the question?

Yes? No?