Difference between revisions of "2006 AMC 10A Problems/Problem 2"

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== Problem ==
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#redirect [[2006 AMC 12A Problems/Problem 2]]
Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>?
 
 
 
<math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
 
== Solution ==
 
Plugging our values into the defined [[operation]], we have
 
 
 
<center><math>\displaystyle h\otimes h = h^3-h</math></center>
 
 
 
Plugging in the [[function]] once more, we have
 
 
 
<center><math>\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h</math></center>
 
 
 
which is choice <math>(C)</math>.
 
 
 
== See also ==
 
{{AMC10 box|year=2006|ab=A|num-b=1|num-a=3}}
 
 
 
[[Category:Introductory Algebra Problems]]
 

Latest revision as of 00:02, 28 April 2008

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