Question

计算多项式4x^2+9y^2+8x-12y+12的值时,取任意x.y的值,发现结果总是正数,请说明理由

Answer 1

4x^2+9y^2+8x-12y+12

=(4x^2+8x+4)+(9y^2-12y+4)+4

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

(2x+2)^2≥0

(3y-2)^2≥0

(2x+2)^2+(3y-2)^2+4＞0

即：4x^2+9y^2+8x-12y+12＞0

所以：无论x,y取何值,4x^2+9y^2+8x-12y+12总是正数.