Question

Tim Max hoac Min:   \(C=-x^2+2xy-4y^2+2x+10y-8\)

Answer 1

\(C=-\left(x^2-2xy+4y^2-2x-10y+8\right)\)

     \(=-\left[\left(x^2-2xy+y^2\right)-2\left(x-y\right)+1+\left(3y^2-9y+3\right)+4\right]\)

       \(=-\left[\left(x-y\right)^2-2\left(x-y\right)+1+3\left(y-1\right)^2+4\right]\)

      \(=-\left[\left(x-y-1\right)^2+3\left(y-1\right)^2+4\right]\)

      \(=-\left[\left(x-y-1\right)^2+3\left(y-1\right)^2\right]-4\le-4\)

          GTLN là -4    tại x=2;y=1