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

Please help me! Thank you.

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    $\begingroup$ Isn't one value obvious to you? (x =27)? For others try converting it to a cubic equation. $\endgroup$ – Rick Aug 31 at 3:07
  • $\begingroup$ 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. $\endgroup$ – Toby Mak Aug 31 at 3:59
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Hint: Let $t=\sqrt[3]x$ and note that $$t^3+t-30=(t-3)(t^2+3t+10).$$

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hint:

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

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