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2013 AMC 12B Problem 6

Problem 6 of 25EasierAlgebra

Real numbers xx and yy satisfy the equation x2+y2=10x−6y−34.x^2 + y^2 = 10x - 6y - 34. What is x+y?x+y?

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Solution

Rearranging gives x2−10x+25+y2+6y+9x^2 - 10x + 25 + y^2 + 6y + 9 =0,= 0, that is (x−5)2+(y+3)2=0.(x-5)^2 + (y+3)^2 = 0. Hence x=5x = 5 and y=−3,y = -3, so x+y=2.x + y = 2. Thus, the correct answer is B.
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Tagged: completing the square

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