Question

How do you solve `x^2>4` using a sign chart?

Answer 1

The answer is `x in ] -oo,-2 [ uu ] 2,+oo [`

Explanation:

Let `f(x)=x^2-4`

Let's rewrite the equation as

`x^2-4=(x+2)(x-2)>0`

Now we can do the sign chart

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

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

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

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

Therefore,

`f(x)>0` when `x in ] -oo,-2 [ uu ] 2,+oo [`