Solve irrational equation $x \sqrt[3]{35-x^3}(x+\sqrt[3]{35-x^3}) = 30$ Solve irrational equation
$$x \sqrt[3]{35-x^3}(x+\sqrt[3]{35-x^3}) = 30$$
Here is what I tried
$t^3 = 35-x^3 \implies x = \sqrt[3]{35-t^3} $
which takes me to nowhere.

See you need $6.5$ in reduced form . So we can just manipulate an get solution . So we need a cubic term to get real number so $x\sqrt{35-x^3}=6$ and $x=3$ gives you $6$ also $x+\sqrt{35-x^3}=5$ where $3$ is the solution thus we have one real answer which is 3 other way is solving by Vieta method.
