Inequality Question

**Stroodle** · July 13th 2009, 01:21 AM

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

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

Thanks for your help

Edit- Oops, wrong thread.

**Plato** · July 13th 2009, 03:01 AM

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.

**mathaddict** · July 13th 2009, 05:29 AM

Originally Posted by Stroodle

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

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

Thanks for your help

Edit- Oops, wrong thread.

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

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

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

Definitely not the best solution .

**Krizalid** · July 13th 2009, 07:47 AM

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.

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