# Inequality

• Oct 3rd 2012, 10:31 AM
skaters
Inequality
would be nice if I could get some help with this.
Attachment 25024
• Oct 3rd 2012, 10:40 AM
johnsomeone
Re: Inequality
Try dividing both sides by the left-hand-side, so it looks like 1 < (3-sqrt(5))^....

Note that 3-sqrt(5) is positive, so the inequality doesn't change when you divide by it, or any power of it. Also, being positive, those exponents are well defined for all x (well, except where x = -1 or x = 1, but that's assumed in writing the problem).

Also note that 3-sqrt(5) < 1. This will effect how it behaves when you raise it to a power.
• Oct 3rd 2012, 10:41 AM
MarkFL
Re: Inequality
Since $3-\sqrt{5}<1$ the inequality implies:

$\frac{x-1}{x+1}<\frac{x+1}{x-1}$