Hello, dhiab!
What a bizarre problem . . .
Solve in We can see that: .
Yet when I solved the inequality algebraically, I got misleading results.
We have: .
Square: .
Simplify: .
Square: .
Simplify: .
This is an upwardopening parabola.
. . When is it above the xaxis?
Find its xintercepts: .
Quadratic Formula: .
The parabola is positive for: .
I realize that Squaring can produce extraneous roots,
. . but "half" of this result is inapplicable.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
This is the upper half of a leftopening parabola with vertex (3,0).
This is the upper half of a rightopening parabola with vertex (1,0).
The question: When is more than a halfunit above ? Code:

* .  *
::::*. *
::::::: *
::::::* *
:::*  *
:*  *
   *   +       *     
1 .  . 3
.  .
. .
 .
.  .
.  .

The solution is the shaded region: .
Edit: Ha! . . . runninggag neat me to it!
.