Difference between revisions of "2000 AMC 12 Problems/Problem 11"
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| + | {{duplicate|[[2000 AMC 12 Problems|2000 AMC 12 #11]] and [[2000 AMC 10 Problems|2000 AMC 10 #15]]}} | ||
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==Problem== | ==Problem== | ||
Two non-zero [[real number]]s, <math>a</math> and <math>b,</math> satisfy <math>ab = a - b</math>. Which of the following is a possible value of <math>\frac {a}{b} + \frac {b}{a} - ab</math>? | Two non-zero [[real number]]s, <math>a</math> and <math>b,</math> satisfy <math>ab = a - b</math>. Which of the following is a possible value of <math>\frac {a}{b} + \frac {b}{a} - ab</math>? | ||
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==See also== | ==See also== | ||
{{AMC12 box|year=2000|num-b=10|num-a=12}} | {{AMC12 box|year=2000|num-b=10|num-a=12}} | ||
| + | {{AMC10 box|year=2000|num-b=14|num-a=16}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 23:54, 26 November 2011
- The following problem is from both the 2000 AMC 12 #11 and 2000 AMC 10 #15, so both problems redirect to this page.
Problem
Two non-zero real numbers, 
and 
satisfy 
. Which of the following is a possible value of 
?
Solution
.
Alternatively, we could test simple values, like 
, which would yield 
.
See also
| 2000 AMC 12 (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 12 Problems and Solutions | |
| 2000 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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 | ||
