数学1、若x,y都是实数，则x平
1、x^2+xy+y^2-3x-3y+1999
=x^2+(y-3)x+(y^2-3y+1999)
=x^2+2x(y-3)/2+(y-3)^2/4]-(y-3)^2/4+(y^2-3y+1999)
=[x+(y-3)/2]^2+(3y^2-6y+3987)/4
=(x+y/2-3/2)62+(3/4)(y-1)^2+996
因为(x+y/2-3/2)^2>=0,(y-1)^2>=0并且当x=1,y=1时等号成立，所以此二元二次多项式的最小值是996。
2）多项式12x^2-10xy+2y^2+11x-5y+m
=2(6x^2-5xy+y^2+11x/2-5y/2+m/2)
=2[(3...全部
1、x^2+xy+y^2-3x-3y+1999
=x^2+(y-3)x+(y^2-3y+1999)
=x^2+2x(y-3)/2+(y-3)^2/4]-(y-3)^2/4+(y^2-3y+1999)
=[x+(y-3)/2]^2+(3y^2-6y+3987)/4
=(x+y/2-3/2)62+(3/4)(y-1)^2+996
因为(x+y/2-3/2)^2>=0,(y-1)^2>=0并且当x=1,y=1时等号成立，所以此二元二次多项式的最小值是996。
2）多项式12x^2-10xy+2y^2+11x-5y+m
=2(6x^2-5xy+y^2+11x/2-5y/2+m/2)
=2[(3x-y)(2x-y)+11x/2-3y/2+m/2]
--->6x^2-5xy+y^2+(2p-3q)x-(p+q)y+pq
=6x^2-5xy+y^2+11x/2-3y/2+m/2。
对比系数得到方程组：2p-3q=11/2,p+q=3/2。得到p=2,q=-1/2。
m/2=pq=2*(-1/2)=-1。
所以m=-2。收起
