Question

How do you solve `–x^2 + 4 < 0`?

Answer 1

The solution is `x in (-oo, -2) uu(2, +oo)`

Explanation:

The inequality is

`-x^2+4<0`

`=>`, `x^2-4>0`

`=>`, `(x+2)(x-2)>0`

Let `y=(x+2)(x-2)`

Build a sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-2` `color(white)(aaaaa)` `2` `color(white)(aaaaa)` `+oo`

`color(white)(aaaa)` `x+2` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `x-2` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `y` `color(white)(aaaaaaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

Therefore,

`y>0` when `x in (-oo, -2) uu(2, +oo)`

graph{-x^2+4 [-7.9, 7.9, -3.95, 3.95]}