Another HW Question Polynomial and Radical Equations

**civiliam** · October 2nd 2008, 11:06 AM

Use factoring to solve the equation for real values of the variables

z^3/2 - 2^1/2 = 0

I think i'm making it harder then it realy is please help

**Sean12345** · October 2nd 2008, 11:42 AM

Hi again civiliam,

We have $z^{\frac{3}{2}}-2^{\frac{1}{2}}=0$ . Now this leads to $z^{\frac{3}{2}}=2^{\frac{1}{2}}$ . Notice that to get $z$ we need to raise $z^{\frac{3}{2}}$ to the power of $\frac{2}{3}$ since we know that $(a^b)^c=a^{bc}$ . Hence raising both sides of the equation to the power $\frac{2}{3}$ yields $z=2^{\left(\frac{1}{2}\right)\left(\frac{2}{3}\rig ht)}=2^{\frac{1}{3}}$ .

Hope this helps.

**icemanfan** · October 2nd 2008, 11:44 AM

This is what I would do:

$z^{3/2} - 2^{1/2} = 0$

$z^{3/2} = 2^{1/2}$

$(z^{3/2})^{2/3} = (2^{1/2})^{2/3}$

$z = 2^{1/3}$

**civiliam** · October 2nd 2008, 11:47 AM

sorry why 2/3?

**icemanfan** · October 2nd 2008, 11:49 AM

Originally Posted by civiliam

sorry why 2/3?

Because 2/3 is the reciprocal of 3/2. When you raise $z^{3/2}$ to the 2/3 power, the exponent on z becomes 1.

**civiliam** · October 2nd 2008, 11:50 AM

ahh I c thank you much!

**civiliam** · October 2nd 2008, 11:54 AM

so i wrote the problem out wrong would I still work it out the same way if the 2^1/2 was z^1/2?

z^3/2 - z^1/2 = 0

**icemanfan** · October 2nd 2008, 11:57 AM

Now you can factor out $z^{1/2}$ .

Beginning with $z^{3/2} - z^{1/2} = 0$ :

$z^{1/2} \cdot (z - 1) = 0$

z = 0 or 1.

So the problem changes significantly.

**civiliam** · October 2nd 2008, 12:02 PM

wow that was simple odd how minor changes to a problem can throw me off so easily thanks again

Thread: Another HW Question Polynomial and Radical Equations

LinkBack

Thread Tools

Display

Another HW Question Polynomial and Radical Equations

Similar Math Help Forum Discussions

Question about radical equations

Radical Equations

Radical Equations

radical equations

Polynomial, Radical Equations & Inequalities. Help needed by Jan. 9,2007!

Search Tags