SOLUTION: x^(2/3) + 2 = 3x^ (1/3)

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Question 1004807: x^(2/3) + 2 = 3x^ (1/3)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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x%5E%282%2F3%29 + 2 = 3x%5E%281%2F3%29.

Introduce new variable y = root%283%2Cx%29. Then your equation takes the form

y%5E2 + 2 = 3y, or

y%5E2 - 3y + 2 = 0.

Solve this quadratic equation. You can use the quadratic formula, or the Viete's theorem, or factoring.

The roots are y = 1 and y = 2.

y = 1 -----> x = 1.

y = 2 -----> x = 8.

Answer. The solutions are x=1 and x=8.