\(C=x^2+2x-y^2+4y-7\)
\(C=x^2+2x-y^2+4x+1-4-4\)
\(C=\left(x^2+2x+1\right)-\left(y^2-4y+4\right)-4\)
\(C=\left(x+1\right)^2-\left(y-2\right)^2-4\)
Vì \(\left(x+1\right)^2\ge0;\left(y-2\right)^2\ge0\)
\(\Rightarrow C=\left(x+1\right)^2-\left(y-2\right)^2-4\ge0-0-4\)
\(\Rightarrow C\ge-4\)
Vậy\(GTNN_C=-4\)tại \(x=-1\)và \(y=2\)