Solve for x... rational exponent x^(5/3) = 1-2x^2?

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

I've tried absolutely everything, I know it has 5 roots, 4 are imaginary, 1 is real.

I need to find the real value.

I've tried using x^(5/6)^2 as my ax^2 term, but it just doesn't fall out into anything nice.

Anonymous2011-05-07T10:46:08Z

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Solution: x ≈ 0.557723

http://www.wolframalpha.com/input/?i=x^%285%2F3%29+%3D+1+-+2x%C2%B2

Multiply each term by x³ and try to solve for x.

Good luck!