SOLUTION: 5x^(1/3) + 3x^(2/3) = 8 Can you help me? I hope I wrote it right; it's 5x to the one third plus 3x to the two thirds. Thank you!

Question 992752: 5x^(1/3) + 3x^(2/3) = 8
Can you help me? I hope I wrote it right; it's 5x to the one third plus 3x to the two thirds. Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5x^(1/3) + 3x^(2/3) = 8
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Rewrite as::
3(x^(1/3))^2 + 5(x^(1/3)) - 8 = 0
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Note:: This is a quadratic equation. The variable is x^(1/3)
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Let x^(1/3) = w
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Rewrite the equation as::
3w^2 + 5w - 8 = 0
Factor::
3w^2 + 8w-3w - 8 = 0
w(3w+8) - (3w+8) = 0
(3w+8)(w-1) = 0
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w = -8/3 or w = 1
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Now, solve for "x"
x^(1/3) = (-8/3) or x^(1/3) = 1
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x = (-8/3)^3 or x = 1^3
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x = -512/27 or x = 1
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Cheers,
Stan H.
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