\(P=x^2+5y^2+4xy-2x-6y+2021=x^2+2x\left(y-1\right)+\left(y-1\right)^2+\left(4y^2-4y+1\right)+2019=\left(x+y-1\right)^2+\left(2y-1\right)^2+2019\ge2019\)
\(minP=2019\Leftrightarrow\)\(x=y=\dfrac{1}{2}\)
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