Difference between revisions of "2005 iTest Problems/Problem 52"
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If the product of <math>(\sqrt2 +\sqrt3+\sqrt5) (\sqrt2 +\sqrt3-\sqrt5) (\sqrt2 -\sqrt3+\sqrt5) (-\sqrt2 +\sqrt3+\sqrt5)</math> is <math>12\sqrt6+ 6\sqrt{x}</math> , find <math>x</math>. | If the product of <math>(\sqrt2 +\sqrt3+\sqrt5) (\sqrt2 +\sqrt3-\sqrt5) (\sqrt2 -\sqrt3+\sqrt5) (-\sqrt2 +\sqrt3+\sqrt5)</math> is <math>12\sqrt6+ 6\sqrt{x}</math> , find <math>x</math>. | ||
| − | + | IMPORTANT NOTE: This problem was thrown out of the actual competition. | |
| + | |||
==Solution (credit to Mathzeus1024)== | ==Solution (credit to Mathzeus1024)== | ||
The entire product computes to <math>24</math>. Thus: | The entire product computes to <math>24</math>. Thus: | ||
Latest revision as of 21:44, 19 October 2025
Problem
If the product of 
is 
, find 
.
IMPORTANT NOTE: This problem was thrown out of the actual competition.
Solution (credit to Mathzeus1024)
The entire product computes to 
. Thus:
;
or ![$x = [4 - 2\sqrt{6}]^2 = 40 - 16\sqrt{6}$](http://latex.artofproblemsolving.com/a/e/f/aef60daf6f8eb15ac5cbea78f2e1b24131395b5d.png)
.
Note: The problem writers intended for it to equal a value where was an integer. This appears to be why it was thrown out.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 51 |
Followed by: Problem 53 | |
| 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 | ||
