# Inequality Question

• Jul 13th 2009, 01:21 AM
Stroodle
Inequality Question
What's the best method for solving these without a graph.

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

• Jul 13th 2009, 03:01 AM
Plato
Quote:

Originally Posted by Stroodle
What's the best method for solving these without a graph.
Find $\displaystyle \left\{ x:x^{\frac{3}{2}}>x^2 \right\}$

It should be clear to you that $\displaystyle x\ge 0$ else $\displaystyle x^{\frac{3}{2}}$ is not defined.
Therefore $\displaystyle x^3>x^4$.
Now go for it.
• Jul 13th 2009, 05:29 AM
Quote:

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

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

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

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

Draw the number line .
THus the solution set is {$\displaystyle {x: 0<x<1 }$}

Definitely not the best solution .
• Jul 13th 2009, 07:47 AM
Krizalid
It's clear that both sides are positive, so you can square them, thus $\displaystyle x^3>x^4\implies x^2\cdot x(x-1)<0.$

I think you can continue.