Tìm GTLN của biểu thức: A = 5 + 2xy + 14y – x^2 – 5y^2 – 2x

* Hướng dẫn giải

$\begin{array}{l}A=5+2xy+14y–x^2–5y^2–2x\\ =–x^2–5y^2+2xy–2x+14y+5\\ =-\left(x^2-2xy-2x+y^2-2y+1\right)-4y^2+12y-9+15\\ =-\left[x^2-2x\left(y-1\right)+y^2-2y+1\right]-{\left(2y-3\right)}^2+15\\ =-\left[x^2-2x\left(y-1\right)+{\left(y-1\right)}^2\right]-{\left(2y-3\right)}^2+15\\ =-\left(x-y+1\right){}^2-{\left(2y-3\right)}^2+15\end{array}$