AMC10 2006 A

AMC10 2006 A · Q2

AMC10 2006 A · Q2. It mainly tests Algebra misc.

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

定义$x \otimes y = x^3 - y$。求$h \otimes (h \otimes h)$的值？

(A) $-h$ $-h$

(B) 0 0

(D) $2h$ $2h$

(E) $h^3$ $h^3$

Answer

Correct choice: (C)

正确答案：（C）

Solution

By the definition we have $$h \otimes (h \otimes h) = h \otimes (h^3 - h) = h^3 - (h^3 - h) = h.$$

根据定义，$$h \otimes (h \otimes h) = h \otimes (h^3 - h) = h^3 - (h^3 - h) = h.$$

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