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2008 AMC 12B Problem 7

Problem 7 of 25EasierAlgebra

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

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Solution

Since (y−x)2=(x−y)2,(y - x)^2 = (x - y)^2, both inputs to the operation are the same value t=(x−y)2.t = (x - y)^2. Therefore (x−y)2$(y−x)2(x - y)^2 \$ (y - x)^2 =t$t= t \$ t =(t−t)2=0.= (t - t)^2 = 0. Thus, the correct answer is A.

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Concepts: custom operation · symmetry

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