Đáp án:
$Min_{2x^2+9y^2-6xy-6x-12y+2046}=2017$ `⇔` $\left \{ {{y=\frac{7}{3}} \atop {x=5}} \right.$
Giải thích các bước giải:
Ta có :
`2x^2+9y^2-6xy-6x-12y+2046`
`=(x^2-6xy+9y^2)+(x^2-10x+25)+(4x-12y)+2021`
`=(x-3y)^2+(4x-12y)+(x-5)^2+2021`
`=(x-3y)^2+4(x-3y)+(x-5)^2+2021`
`=[(x-3y)^2+2.(x-3y).2+2^2]+(x-5)^2+2017`
`=(x-3y+2)^2+(x-5)^2+2017≥2017`
Dấu ''='' xảy ra khi :
$\left \{ {{x-3y+2=0} \atop {x-5=0}} \right.$
`→` $\left \{ {{y=\frac{7}{3}} \atop {x=5}} \right.$
Vậy $Min_{2x^2+9y^2-6xy-6x-12y+2046}=2017$ `⇔` $\left \{ {{y=\frac{7}{3}} \atop {x=5}} \right.$
