Answer

`x^2 - 4x + y^2 - 6y + 15 = 2`

`<=> x^2 - 4x + y^2 - 6y + 4 + 9 + 2 = 2`

`<=> (x^2 - 4x + 4) + (y^2 - 6y + 9) = 2 - 2`

`<=> (x^2 - 2 . x . 2 + 2^2) + (y^2 - 2 . y . 3 + 3^2) = 0`

`<=> (x - 2)^2 + (y - 3)^2 = 0`

Nhận xét:

`(x - 2)^2 >= 0 AA x`

`(y - 3)^2 >= 0 AA y`

`=> (x - 2)^2 + (y - 3)^2 >= 0 AA x , y`

Dấu $"="$ xảy ra:

`<=>` $\begin{cases} x - 2 = 0\\y - 3 = 0 \end{cases}$

`<=>` $\begin{cases} x = 0 + 2\\y = 0 + 3 \end{cases}$

`<=>` $\begin{cases} x = 2\\y = 3 \end{cases}$

Vậy `(x , y) = (2 , 3).`

Trả lời :

    ` x² - 4x + y² - 6y + 15 = 2`

 ⇔` ( x² - 4x + 4 ) + ( y² - 6y + 9 ) + 2 = 2`

 ⇔ ` ( x - 2 )² + ( y - 3 )² = 0`

 ⇔  $\left \{ {{x - 2 = 0} \atop {y - 3 = 0}} \right.$ 

 ⇔ $\left \{ {{x = 2} \atop {y=3}} \right.$ 

    Vậy......