2006 AMC 12A Problems/Problem 2: Difference between revisions

Revision as of 21:03, 11 July 2006

Define $x\otimes y=x^3-y$ . What is $h\otimes (h\otimes h)$ ?

$\mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h$

$\mathrm{(E) \ } h^3$

By the definition of $\otimes$ , we have $h\otimes h=h^{3}-h$ . Then $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=h$ . The answer is C.

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 == Solution ==
-Using 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 C.
+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 C.
 == See also ==
 * [[2006 AMC 12A Problems]]