Question

x,y是实数,代数式2x平方-6xy+5y平方+6x-12y+11的最小值为多少?

Answer 1

2X^2-6XY+5Y^2+6X-12Y+11

=2X^2-6XY+5Y^2+6（x-2y）+11

=(x^2-4xy+4y^2)+(x^2-2xy+y^2)+6(x-2y)+11

=(x-2y)^2+6(x-2y)+9 +(x-y)^2 +2

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