# variable r,r,t

#### jacks

##### Well-known member
Calculate number $r,s,t$ in $\displaystyle \sqrt[3]{\sqrt[3]{2} - 1} = \sqrt[3]{r} + \sqrt[3]{s} + \sqrt[3]{t}$

where $r,s,t \in Q$

#### Sudharaka

##### Well-known member
MHB Math Helper
Calculate number $r,s,t$ in $\displaystyle \sqrt[3]{\sqrt[3]{2} - 1} = \sqrt[3]{r} + \sqrt[3]{s} + \sqrt[3]{t}$

where $r,s,t \in Q$
Hi jacks,

Can you please tell me where you encountered this problem? Is this a equation that you obtained as a consequence of your research/project, or is it a question from a book?

Kind Regards,
Sudharaka.

#### Opalg

##### MHB Oldtimer
Staff member
Calculate number $r,s,t$ in $\displaystyle \sqrt[3]{\sqrt[3]{2} - 1} = \sqrt[3]{r} + \sqrt[3]{s} + \sqrt[3]{t}$

where $r,s,t \in Q$
I found that $\sqrt[3]{\mathstrut\sqrt[3]{2} - 1} = \sqrt[3]{\frac19} + \sqrt[3]{-\frac29} + \sqrt[3]{\frac49}$. I did this more or less by trial and error, so the method is not very revealing. But you can verify that it is correct by cubing both sides.