Difference between revisions of "2006 AMC 12A Problems/Problem 2"
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== Problem == | == Problem == | ||
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Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>? | Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>? | ||
| − | <math> \mathrm{(A) \ | + | <math>\mathrm{(A)}\ -h\qquad\mathrm{(B)}\ 0\qquad\mathrm{(C)}\ h\qquad\mathrm{(D)}\ 2h \mathrm{(E)}\ h^3</math> |
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== Solution == | == Solution == | ||
| − | + | By the definition of <math>\otimes</math>, we have <math>h\otimes h=h^{3}-h</math>. Then <math>h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=h</math>. The answer is <math>\mathrm{(C)}</math>. | |
| − | By the definition of <math>\otimes</math>, we have <math>h\otimes h=h^{3}-h</math>. | ||
== See also == | == See also == | ||
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{{AMC12 box|year=2006|ab=A|num-b=1|num-a=3}} | {{AMC12 box|year=2006|ab=A|num-b=1|num-a=3}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 23:35, 27 April 2008
Problem
Define 
. What is 
?
Solution
By the definition of 
, we have 
. Then 
. The answer is 
.
See also
| 2006 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 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 | |
