How Do You Solve the Inequality |4 + 2r - r^2| < 1?

[rsaad]

Homework Statement

|4 + 2r - r^2| <1

Homework Equations

4 + 2r - r^2 = (r - (1+ √5) ) (r - (1 - √5))

The Attempt at a Solution

I tried to use the roots but no use. How should I proceed?

 

[tia89]

First of all you have to take away the absolute value... this means that you have to solve a system of inequalities.
Indeed if the quantity in the abs val is negative, then you will have to change sign, and if it is positive you can take away the abs val without problems.

As an example, in general when you want to solve $|x|<a$ you do the following:
solve
$$ \begin{cases} x\geq 0 \\ x<a \end{cases} $$
Then solve
$$ \begin{cases} x<0 \\ -x<a \end{cases} $$
(this because in case x is negative then you can take away the abs val but you have to change sign)
When done, just combine the solutions and you are done

 

[Ray Vickson]

Homework Statement

|4 + 2r - r^2| <1

Homework Equations

4 + 2r - r^2 = (r - (1+ √5) ) (r - (1 - √5))

The Attempt at a Solution

I tried to use the roots but no use. How should I proceed?

Start by drawing a graph of the function f(r) = 4 + 2r - r^2.