Difference between revisions of "2013 AMC 12B Problems/Problem 6"
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== See also == | == See also == | ||
| + | {{AMC10 box|year=2013|ab=B|num-b=10|num-a=12}} | ||
{{AMC12 box|year=2013|ab=B|num-b=5|num-a=7}} | {{AMC12 box|year=2013|ab=B|num-b=5|num-a=7}} | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
[[Category:Algebraic Manipulations Problems]] | [[Category:Algebraic Manipulations Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:46, 3 February 2015
- The following problem is from both the 2013 AMC 12B #6 and 2013 AMC 10B #11, so both problems redirect to this page.
Problem
Real numbers 
and 
satisfy the equation 
. What is 
?
Solution
If we complete the square after bringing the and terms to the other side, we get 
. Squares of real numbers are nonnegative, so we need both 
and 
to be 
which only happens when 
and 
. Therefore, 
See also
| 2013 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
| 2013 AMC 12B (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
