# Solving $x + \sqrt[3]{x} = 30$ [closed]

If $$x + \sqrt[3]{x} = 30$$, then what is the value of $$x$$?

Please help me! Thank you.

• Isn't one value obvious to you? (x =27)? For others try converting it to a cubic equation.
– Rick
Aug 31 '19 at 3:07
• Once you notice that $x=27$ is a solution, notice that $x$ is a monotonically increasing function, and $x^{1/3}$ also is monotonic, so $x+x^{1/3}$ as a whole is monotonic. Aug 31 '19 at 3:59

## 2 Answers

Hint: Let $$t=\sqrt[3]x$$ and note that $$t^3+t-30=(t-3)(t^2+3t+10).$$

hint:

$$x^{1/3}=30-x$$ can nicely be written if you raise both sides to the power of three.