AMC12 2008 B

AMC12 2008 B · Q7

AMC12 2008 B · Q7. It mainly tests Manipulating equations.

For real numbers $a$ and $b$, define $a \$ b = (a - b)^2$. What is $(x - y)^2\$(y - x)^2$?

对实数 $a$ 和 $b$，定义 $a\$ b = (a - b)^2$。求 $(x - y)^2\$(y - x)^2$ 的值。

(A) 0 0

(B) $x^2 + y^2$ $x^2 + y^2$

(D) $2y^2$ $2y^2$

(E) 4xy 4xy

Answer

Correct choice: (A)

正确答案：（A）

Solution

$\left[ (x-y)^2 - (y-x)^2 \right]^2$ $\left[ (x-y)^2 - (x-y)^2 \right]^2$ $[0]^2$ $0 \Rightarrow \textbf{(A)}$

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