Difference between revisions of "1993 AHSME Problems/Problem 4"
(Created page with "== Problem == Define the operation "<math>\circ</math>" by <math>x\circ y=4x-3y+xy</math>, for all real numbers <math>x</math> and <math>y</math>. For how many real numbers <math...") |
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== Solution == | == Solution == | ||
| − | <math>\fbox{E}</math> | + | |
| + | Note that <math>3 \circ y = 4(3) - 3(y) + (3)(y) = 12 - 3y + 3y = 12</math> for all values of <math>y</math>. This implies that the answer is <math>\fbox{E}</math>, more than four solutions. | ||
== See also == | == See also == | ||
Revision as of 23:49, 27 November 2018
Problem
Define the operation "
" by 
, for all real numbers 
and 
. For how many real numbers does 
?
Solution
Note that 
for all values of . This implies that the answer is 
, more than four solutions.
See also
| 1993 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
