2006 AMC 12A Problems/Problem 2

Revision as of 17:25, 16 December 2021 by Dairyqueenxd (talk | contribs) (Solution 2)
The following problem is from both the 2006 AMC 12A #2 and 2006 AMC 10A #2, so both problems redirect to this page.

Problem

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

$\textbf{(A)}\ -h\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ h\qquad\textbf{(D)}\ 2h\qquad\textbf{(E)}\ h^3$

Solution 1

By the definition of $\otimes$, we have $h\otimes h=h^{3}-h$.

Then, $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=\boxed{\textbf{(C) }h}.$

Solution 2

Substitute $1$ for $h$. You get $1^3-(1^3-1)$ which is $1$. Since h=1, the answer is $\boxed{\textbf{(C) }h}.$

~dragoon also aop is a god

See also

2006 AMC 12A (ProblemsAnswer KeyResources)
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
2006 AMC 10A (ProblemsAnswer KeyResources)
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 10 Problems and Solutions

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