Question

Solve for x? x^2/3 – 2x^1/3 – 8 = 0

Answer 1

let u=x^{1/2}

Answer 2

if you do this what do you get?

Answer 3

Hmm.. I seem to be having trouble with this still. I'm not quite sure how to set it up. I'm pretty lost with it. :P Thanks for helping.

Answer 4

actually i mean't if you let u=x^{1/3}

Answer 5

if you do that you get

\[u^2-2u-8=0\]

Answer 6

Sooo... it told me to solve for x, so how exactly did the u come in? I'm sorry. My brain is kind of shutting down right now after so many hours of math work. :P

Answer 7

u is just a variable to simplify the problem

Answer 8

Oh, okay. :) That makes sense.

Answer 9

so now you have

\[u^2-2u-8\]

can you factor this?

Answer 10

Yes. Is this right? (u-4)(u+2)

Answer 11

yep

Answer 12

so now your roots are 4 and -2 (from the equations u-4=0 and u+2=0)

Answer 13

however these are the roots for u so now you have to plug these into

\[u=x^{1/3}\]

Answer 14

you get

\[4=x^{1/3}\]
\[-2=x^{1/3}\]

Answer 15

Ohh.... okay. :) So what would I go about doing at this point then?

Answer 16

cube both sides to get x by itself

Answer 17

\[4^3=(x^{1/3})^3\]

Answer 18

\[64=x\]

Answer 19

now for the next one you

have

\[-2^3=(x^{1/3})^3\]

Answer 20

\[-8=x\]

Answer 21

so your solution set is

[64,0],[-8,0]

Answer 22

Awesome. :) I really appreciate your help on this SOOOOO much. Thank you, thank you, thank you.

Answer 23

no problem :)

Answer 24

So if I close this question will you still be given a medal? This is my first time asking a question and I certainly want you to be rewarded for your help. :)

Answer 25

yes you can close if you like