Difference between revisions of "1997 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | Given a nonnegative real number <math>x</math>, let <math>\langle x\rangle</math> denote the fractional part of <math>x</math>; that is, <math>\langle x\rangle=x-\lfloor x\rfloor</math>, where <math>\lfloor x\rfloor</math> denotes the greatest integer less than or equal to <math>x</math>. Suppose that <math>a</math> is positive, <math>\langle a^{-1}\rangle=\langle a^2\rangle</math>, and <math>2<a^2<3</math>. Find the value of <math>a^{12}-144a^{-1}</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1997|num-b=8|num-a=10}} | |
Revision as of 14:33, 20 November 2007
Problem
Given a nonnegative real number 
, let 
denote the fractional part of ; that is, 
, where 
denotes the greatest integer less than or equal to . Suppose that 
is positive, 
, and 
. Find the value of 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1997 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
