Question

Tìm giá trị lớn nhất:P=\(\dfrac{2012}{x^2+y^2+20\left(x+y\right)+2213}\)

Answer 1

\(P=\dfrac{2012}{\left(x^2+20x+100\right)+\left(y^2+20y+100\right)+2013}\)

\(P=\dfrac{2012}{\left(x+10\right)^2+\left(y+10\right)^2+2013}\le\dfrac{2012}{2013}\)

Dấu "=" xảy ra khi \(x=y=-10\)