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September 30, 2014

September 30, 2014

Posted by **Unknown** on Wednesday, August 29, 2012 at 5:03am.

1.2x^2/3+5^1/3=12

2. 6x^6/3-5x^1/3-6=0

- Algebra2 -
**Reiny**, Wednesday, August 29, 2012 at 9:08am#1

2x^(2/3) + 5x^(1/3) = 12 , you have a typo

let x^(1/3) = y

your equation becomes

2y^2 + 5y - 12 = 0

(2y-3)(y+4) = 0

y = 3/2 or y = -4

then x^(1/3) = 3/2 ---- x = 27/8

if x^(1/3) = -4 ----> x = -64

check:

if x = 27/8

LS = 2(27/8)^(2/3) + 5(7/8)^(1/3)

= 2(9/4) + 5(3/2)

= 9/2 + 15/2 = 12 = RS

if x = -64

LS = 2(-64)^(2/3) + 5(-64)^(1/3)

= 2(16) - 5(-4)

≠ RS

x = 27/8

(in y = x^(1/3) , x would be defined as x>0

enter 2x^(2/3)+5x^(1/3)-12 into "first graph" of

http://rechneronline.de/function-graphs/

to see what I mean. There will be only one solution at x = 27/8 )

----------

I think you have a typo in #2 if the question is supposed to be the same type

It should probably say

6x^(2/3) - 5x^(1/3) - 6 = 0

try #2 in the same way by letting y = x^(1/3)

it also factors, remember to reject a negative value of y

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