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  4. Suppose x and y are real numbers satisfying the equation x2+y2-22 x-20 y+221=0. The value of x y is

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Q. Suppose $x$ and $y$ are real numbers satisfying the equation $x^2+y^2-22 x-20 y+221=0$. The value of $x y$ is

Complex Numbers and Quadratic Equations

Solution:

$( x -11)^2+( y -10)^2=0 $
$\Rightarrow x = 11 \text { and } y =10 \Rightarrow xy =110 $