Given $x^3+x-1 = 0$, what's the value of $x^3+2x^2$ Given $x^3+x-1 = 0$, what's the value of $x^3+2x^2$?
obviously $$x^3+2x^2 = 2x^2-x+1$$ but it can't be refactor. Unable to observe anything interesting either. 
The numerical solution also doesn't look interesting. 
https://www.wolframalpha.com/input/?i=x%5E3%2Bx-1
any other thoughts?
 A: Answers to some problems in mathematics are really ugly and probably look uninteresting too. Nobody can help that. If you are looking for something interesting, I can give you the following text. The expression for the only real root of the equation $x^3+x-1=0$ is, 
$$x=\frac{2}{\sqrt{3}}\sinh\left(\frac{1}{3}\sinh^{-1}\left(\frac{3\sqrt{3}}{2}\right)\right)=0.68232780382801932736948373971105.$$
Therefore the Wolfram-Alpha is correct. Now, you want to know the value of $x^3+2x^2$. Let,
$$x^3+2x^2=2x^2-x+1=k$$
We can express $k$ as,
$$k=\frac{7+\left(4x-1\right)^2}{8}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space$$
$$=\frac{21+\left(8\sinh\left(\frac{1}{3}\sinh^{-1}\left(\frac{3\sqrt{3}}{2}\right)\right)-\sqrt{3}\right)^2}{24} \tag{1}$$
$$=1.2488146599255167259439787107289.\space$$
Once again the Wolfram-Alpha is correct (see the comment from  Matthew Daly). 
Now, if (1) does not look interesting enough, then there is nothing else I can do.
