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variable r,r,t

jacks

Well-known member
Apr 5, 2012
226
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
Feb 5, 2012
1,621
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
Feb 7, 2012
2,706
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.