Question

当X,Y为何值时,代数式x^2+y^2+4x-6y+15有最小值,并求出最小值.

Answer 1

因为x^2+y^2+4x-6y+15

=x^2+4x+4+y^2-6y+9+2

=(x+2)^2+(y-3)^2+2 ,

(x+2)^2≥0,(y-3)^2≥0,

所以当x=-2,y=3时,(x+2)^2+(y-3)^2+2有最小值,最小值是2