Difference between revisions of "2007 Alabama ARML TST Problems/Problem 9"
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We can see the pattern: | We can see the pattern: | ||
− | <math>F_{n}x+F_{n+1}y=-1^{n-1}F_{2011-n}</math> | + | <math>F_{n}x+F_{n+1}y=(-1)^{n-1}F_{2011-n}</math> |
Thus | Thus |
Latest revision as of 08:29, 27 August 2008
Problem
Let , and
for
. Find the value of
such that
is the
-coordinate of the intersection between the linear equations
Solution
We subtract equations:
We can see the pattern:
Thus
Therefore and
.
See also
2007 Alabama ARML TST (Problems) | ||
Preceded by: Problem 8 |
Followed by: Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |