Quadratic Equation but with Fractional Powers

Question

I've got the equation I'm trying to solve:

$x^{2/3}+3x^{1/3}-10=0$

But don't really know where to go. I've been kind of trying something like:

${3\sqrt x^2} + {3\sqrt x} - 10 = {3\sqrt 0}$

Answer 1

If you make the substitution $u = x^{1/3}$ then you have $u^2 = (x^{1/3})^2 = x^{2/3 }$.

Your equation $x^{2/3}+3x^{1/3}-10=0$ becomes $u^2+3u-10=0$.

Solve this equation to give $u=\ldots$ , then reverse the substitution to give $x^{1/3} = \ldots$

Finally, cube both sides to give $x = \ldots$

(There will be two solutions.)