giúpppppppppppppppp vs ạ :((

`C = 2x^2 + y^2 - 2xy + x+2`

`= x^2 + x^2 + y^2 - 2xy + x + 1/4 + 7/4`

`= (x^2 + x + 1/4) + (x^2 - 2xy + y^2) + 7/4`

`= (x + 1/2)^2 + (x-y)^2 + 7/4`

Do `(x + 1/2)^2 >= 0 AA x`

Và `(x-y)^2 >=0 AA x`

`=> (x + 1/2)^2 + (x-y)^2 >= 0 AA x`

`<=> (x + 1/2)^2 + (x-y)^2 + 74 >= 0 + 7/4 AA x`

Hay `C >= 7/4 AA x`

Dấu $"="$ xảy ra khi:

$\begin{cases} (x+\dfrac{1}{2})^2=0\\(x-y)^2=0 \end{cases}$

`<=>` $\begin{cases} x+\dfrac{1}{2}=0\\x-y=0 \end{cases}$

`<=>` $\begin{cases} x=\dfrac{-1}{2}\\x=y \end{cases}$

`<=> x=y=\frac{-1}{2}`

Vậy `C_{min} = 7/4 <=> x - y = (-1)/2`