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I Have Forgotten My Algebra!

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Okay. So I was helping a friend with some homework the other night, and couldn't figure it out. And even though it's not my homework, it is now going to bug me until I figure it out!

x^(2/3)-2x^(1/3)-3=0

Now my thought was the following...
Add 3 to each side.

x^(2/3)-2x^(1/3)=3

Raise each side to a power of 3... and this is apparently where I messed up.

(x^(2/3)-2x^(1/3))^3=3^3

What am I doing wrong at this point? What should the answer be, or what should I have done? Someone please take me step-by-step through this, or my over analytical mind that won't let go of things might just explode. I'm pretty sure this even invaded my dreams last night, and I'm not even the one with the homework! How sad is that?? In case anyone is wondering how I knew I did it wrong, I found the answer on-line, but couldn't figure out how they got it.
 Jun 24, 2012

4+0 Answers

 #1
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Now look what we have
( dnt try to multyply....bcz it always make more tricky, multiply shud be our last weapon if nothing gonna work )

x^(2/3)-2x^(1/3)-3=0

it s similar to a^2-2ab+b^2=0 i.e. (a-b)^2=0

so try to make it in this form of ( a-b)^2

STEP1. x^(2/3) -2x^(1/3) -3=0
STEP2 x^(2/3) -2x^(1/3) +1-4=0 ( -3 can be wrttn as +1-4= -3 )
STEP3 (x^1/3)^2 -2x^(1/3)+1 -4=0
STEP4 { x^(1/3) -1}^2 -4=0 ( its in the form of (a-b)^2 )
STEP5 { x^(1/3) -1}^2 = 4
STEP6 { x^(1/3) -1}^2 = 2^2 ( 4 is square of 2 )

Removing square from both sides

{ x^(1/3) -1} = 2
x^(1/3) = 2+1
x^(1/3) = 3
x = 3^3
x= 27


Ans. x = 27 ( Crosscheck puttn x=27 in question)
 Jun 25, 2012
 #2
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Let x^(1/3)=y

Thus y^2- 2y -3 = 0
Factor (y-3)(y+1) = 0

Thus y=3 or y= -1
Thus x^(1/3)=3 or x^(1/3)= -1

Thus x=27 or x= -1
 Jun 26, 2012
 #3
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HELLOOOO.......
 Jun 30, 2012
 #4
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Allison:

Okay. So I was helping a friend with some homework the other night, and couldn't figure it out. And even though it's not my homework, it is now going to bug me until I figure it out!

x^(2/3)-2x^(1/3)-3=0

Now my thought was the following...
Add 3 to each side.

x^(2/3)-2x^(1/3)=3

Raise each side to a power of 3... and this is apparently where I messed up.

(x^(2/3)-2x^(1/3))^3=3^3

What am I doing wrong at this point? What should the answer be, or what should I have done? Someone please take me step-by-step through this, or my over analytical mind that won't let go of things might just explode. I'm pretty sure this even invaded my dreams last night, and I'm not even the one with the homework! How sad is that?? In case anyone is wondering how I knew I did it wrong, I found the answer on-line, but couldn't figure out how they got it.





{x=27, x^(1/3)=-1}
 Jun 30, 2012

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