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

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Answer 1 · 2016-12-16T12:46:34

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

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 $x in ] -oo,-2 [ uu ] 2,+oo [$

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