SOLUTION: 30x^2/3-4x^1/3-2=0

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Question 357880: 30x^2/3-4x^1/3-2=0
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
you need to be clearer as to what you want.
I am going to guess that you want to solve for x
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Let y=x%5E%281%2F3%29
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rewrite your equation
30x%5E%282%2F3%29-4x%5E%281%2F3%29-2=0 to
30y%5E2-4y-2=0
use quadratic equation to solve for y
a=30, b=-4, c=-2
y=%28-%28-4%29-Sqrt%28%28-4%29%5E2-4%2A30%2A%28-2%29%29%29%2F%282%2A30%29 or y=%28-%28-4%29%2BSqrt%28%28-4%29%5E2-4%2A30%2A%28-2%29%29%29%2F%282%2A30%29
y=-12/60=-1/5 or y=20/60=1/3
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since y=x%5E%281%2F3%29 then
x%5E%281%2F3%29=-1%2F5 or x%5E%281%2F3%29=1%2F3
X=%28-1%2F5%29%5E3=-1%2F125 or x=%281%2F3%29%5E3=1%2F27
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you should validate the answers by substituting the x values back in the original equation to verify if one or both work