Difference between revisions of "2014 AIME I Problems/Problem 6"
| Line 4: | Line 4: | ||
== Solution == | == Solution == | ||
| − | + | We use the fact that 2013 and 2014 are y-intercepts by plugging them into the equations to get <math>2013=3h^2+j</math> and <math>2014=2h^2+k.</math> | |
== See also == | == See also == | ||
{{AIME box|year=2014|n=I|num-b=5|num-a=7}} | {{AIME box|year=2014|n=I|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:16, 14 March 2014
Problem 6
The graphs 
and 
have y-intercepts of 
and 
, respectively, and each graph has two positive integer x-intercepts. Find 
.
Solution
We use the fact that 2013 and 2014 are y-intercepts by plugging them into the equations to get 
and 
See also
| 2014 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
