Question

配方法求最小值多项式5x²-4xy+4y²+12x+25的最小值是.

Answer 1

5x²-4xy+4y²+12x+25

=x²-4xy+4y²+4x^2+12x+25

=(x-2y)^2+4(x^2+3x)+25

=(x-2y)^2+4(x^2+3x+9/4)+25-9

=(x-2y)^2+4(x+3/2)^2+16

≥16

最小值是16