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2006 AMC 10A Problem 11

Problem 11 of 25IntermediateAlgebraGeometry

Which of the following describes the graph of the equation (x+y)2=x2+y2?(x + y)^2 = x^2 + y^2?

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Solution

Expanding, x2+2xy+y2=x2+y2,x^2 + 2xy + y^2 = x^2 + y^2, which reduces to 2xy=0,2xy = 0, i.e. xy=0.xy = 0. This holds exactly when x=0x = 0 or y=0,y = 0, the two coordinate axes, so the graph is two lines. Thus, the correct answer is C.

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Concepts: algebraic manipulation · coordinate geometry

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