question about inequalities with negative numbers and square roots

let's say you have an inequality such as this:

-1< -2x^{2} < 1 and it reduces to 1/square root of 2 > x > -1/square root of 2

I understand why the inequalities can flip around but I forgot why you don't end with an imaginary number due to taking

the square root of a negative number.

Re: question about inequalities with negative numbers and square roots

Quote:

Originally Posted by

**matnov** let's say you have an inequality such as this:

-1< -2x^{2} < 1 and it reduces to 1/square root of 2 > x > -1/square root of 2

Note that $\displaystyle -1<-2x^2<1$ can be written as $\displaystyle |-2x^2|<1$ so $\displaystyle |x|<\frac{\sqrt{2}}{2}$.

Re: question about inequalities with negative numbers and square roots

thank you, I think I understand. great site by the way - but can anyone refer me to some free software that will let me post mathematical notation on this forum? thanks

Re: question about inequalities with negative numbers and square roots

Quote:

Originally Posted by

**matnov** thank you, I think I understand. great site by the way - but can anyone refer me to some free software that will let me post mathematical notation on this forum? thanks

It is LaTeX. Go to the LaTeX subforum.