Difference between revisions of "2005 iTest Problems/Problem 23"
(→See Also) |
(→See Also) |
||
| Line 8: | Line 8: | ||
==See Also== | ==See Also== | ||
{{iTest box|year=2005|num-b=22|num-a=24}} | {{iTest box|year=2005|num-b=22|num-a=24}} | ||
| + | |||
| + | [[Category: Introductory Algebra Problems]] | ||
Latest revision as of 19:12, 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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
