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Aus Online Mathematik Brückenkurs 1

We rewrite the equation in standard by completing the square for the x- and y-terms:

x2−2x=x−12−12 

y2+2y=y+12−12 

Now, the equation is

x−12−1+y+12−1=−2x−12+y+12=0

The only point which satisfies this equation is xy=1−1  because, for all other values of x and y , the left-hand side is strictly positive and therefore not zero.