Problem

$x^{2}+y^{2}-10 x-2 x+17=0$

Answer

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Answer

Since the equation represents a circle with radius \(\sqrt{44}\), there is no unique solution for x and y, and thus, no unique value for x+y

Steps

Step 1 ：Rewrite the equation as \(x^2 - 12x + y^2 - 10y + 17 = 0\)

Step 2 ：Complete the square in x and y, we get \((x - 6)^2 - 36 + (y - 5)^2 - 25 + 17 = 0\)

Step 3 ：Simplify the equation, \((x - 6)^2 + (y - 5)^2 = 44\)

Step 4 ：Since the equation represents a circle with radius \(\sqrt{44}\), there is no unique solution for x and y, and thus, no unique value for x+y

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