# Math Help - Inequality Question

1. ## Inequality Question

What's the best method for solving these without a graph.

Find $\left\{ x:x^{\frac{3}{2}}>x^2 \right\}$

2. Originally Posted by Stroodle
What's the best method for solving these without a graph.
Find $\left\{ x:x^{\frac{3}{2}}>x^2 \right\}$
It should be clear to you that $x\ge 0$ else $x^{\frac{3}{2}}$ is not defined.
Therefore $x^3>x^4$.
Now go for it.

3. Originally Posted by Stroodle
What's the best method for solving these without a graph.

Find $\left\{ x:x^{\frac{3}{2}}>x^2 \right\}$

$x^{\frac{3}{2}}-x^2>0$

$
x^{\frac{3}{2}}(1-x^{\frac{1}{2}})>0
$

Draw the number line .
THus the solution set is { ${x: 0}

Definitely not the best solution .

4. It's clear that both sides are positive, so you can square them, thus $x^3>x^4\implies x^2\cdot x(x-1)<0.$

I think you can continue.