- #1

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## Homework Statement

Find all numbers x for which

x

^{2}+x+1 > 2 or x

^{2}+x-1>0

## Homework Equations

none

## The Attempt at a Solution

essentially what I did is used the quadratic formula and I got x= [tex]\frac{-1\pm\sqrt{5}}{2}[/tex]

then I graphed the function and found that x

^{2}+x-1 > 0 when x < [tex]\frac{-1-\sqrt{5}}{2}[/tex] or when x > [tex]\frac{-1+\sqrt{5}}{2}[/tex]

I'm asking if there is a non-graphical method to solving this. It's a simple algebra question I don't remember how to solve.

This is from Spivak's calculus 3ed, ch 1 problem 4 vi.