Difference between revisions of "2005 iTest Problems/Problem 23"
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Revision as of 16:45, 13 October 2025
Problem
![$\sqrt[3]{x+\sqrt[3]{x+\sqrt[3]{x+ \sqrt[3]{x ...}}}}= 8$](http://latex.artofproblemsolving.com/d/6/9/d695fde33320acb6d06f4be069091dea9fda5f17.png)
. Find 
.
Solution 1
Cube both sides. Rearranging, we find that ![$512-x=\sqrt[3]{x+\sqrt[3]{x+\sqrt[3]{x...}}}$](http://latex.artofproblemsolving.com/c/0/a/c0a34b21d3600182e2a11978652e2fd32f0ecb4e.png)
.
By the condition of the problem, the expression on the right is also equal to 
. This means that 
. Solving this equation for , we find that 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 22 |
Followed by: Problem 24 | |
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