`Q=(x-1)^2 + (y+2)^2+ (x+y)^2 + 2017` Tìm Min

1 bình luận về “`Q=(x-1)^2 + (y+2)^2+ (x+y)^2 + 2017` Tìm Min”

1. Q=x^2+2xy+y^2+x^2-2x+1+y^2+4y+4+2017
   =2x^2+2xy-2x+2y^2+4y+2022
   => 2Q=4x^2+4xy-4x+4y^2+8y+4044
   =4x^2+2x(y-1)+(y-1)^2+4y^2+8y+4044-(y-1)^2
   =(2x+y-1)^2+4y^2+8y+4044-y^2+2y-1
   =(2x+y-1)^2+3y^2+10y+4043
   =(2x+y-1)^2+3(y^2+2.x. 5/3+25/9+12104/9)
   =(2x+y-1)^2+3(y+5/3)^2+12104/3
   >=12104/3

   => Q>=12104/3 : 2=6052/3
   Dấu $”=”$ <=> {(2x+y-1=0),(y+5/3=0):}

   <=> {(x=4/3),(y=-5/3):}

   Vậy Q_(min)=6052/3 <=> x=4/3;y=-5/3

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