Có: 4H(x)=\((2x)^2\)−2.2x.y+\(y^2\)+\(3y^2\) −4x+4y+4

\(= \left(\right. 2 x - y \left.\right)^{2} - 2 \left(\right. 2 x - y \left.\right) + 3 y^{2} + 2 y + 3 + 1\)

\(= \left(\right. 2 x - y - 1 \left.\right) + 3 \left(\right. y^{2} + \frac{2}{3} y + 1 \left.\right)\)

\(=\left(\right.2x-y-1\left.\right)+3\left(y+\frac12\right.)^2+\frac{8}{3}\geq\frac{8}{3}\).

Vậy giá trị nhỏ nhất của \(E\) là: \(\frac{8}{3}:4=\frac{2}{3}\) tại \(x=\frac{2}{3};y=-\frac{1}{3}\)

I really like life in the countryside because it is peaceful and simple. The air is fresh, and the scenery is beautiful with many trees, rivers, and paddy fields. People in the countryside are friendly and supportive. There is less traffic and noise than in the city. However, sometimes life in the countryside can be a bit boring because there are not many places to go or things to do. There are also fewer schools and hospitals. But overall, I enjoy the simple and calm life there.