SOLUTION: x^(-4/3)-13x^(-2/3)=-36 Can you please help me solve this?

Question 508588: x^(-4/3)-13x^(-2/3)=-36 Can you please help me solve this?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^(-4/3)-13x^(-2/3)=-36
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Your problem is a quadratic form with variable x^(-2/3)
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Let w = x^(-2/3)
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Substitute to get:
w^2 - 13w + 36 = 0
w^2 -9w-4w + 36 = 0
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w(w-9) -4(w-9) = 0
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= (w-9)(w-4) = 0
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w = 9 or w = 4
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Solve for "x":
x^(-2/3) = 9 or x^(-2/3) = 4
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x^(2/3) = 1/9 or x^(2/3) = 1/4
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x = (1/9)^(3/2) or x = (1/4)^(3/2)
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x = 1/27 or x = 1/8
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Cheers,
Stan H.
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