AMC10 2008 B

AMC10 2008 B · Q5

AMC10 2008 B · Q5. It mainly tests Absolute value, Algebra misc.

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

对于实数 $a$ 和 $b$，定义 $a \triangle b = (a - b)^2$。求 $(x \triangle y) \triangle (y \triangle x)$ 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

Answer (A): Note that $(y-x)^2=(x-y)^2$, so $$(x-y)^2\$(y-x)^2=(x-y)^2\$(x-y)^2=\left((x-y)^2-(x-y)^2\right)^2=0^2=0.$$

答案（A）：注意到 $(y-x)^2=(x-y)^2$，所以 $$(x-y)^2\$(y-x)^2=(x-y)^2\$(x-y)^2=\left((x-y)^2-(x-y)^2\right)^2=0^2=0。$$

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