Question

关于x,y多项式6mx²+4nxy+2x+2xy-x²+y+4不含二次项

关于x,y多项式6mx²+4nxy+2x+2xy-x²+y+4不含二次项，求多项式2m²n+10m-4n+2-2m²n-4m+2n的值.

Answer 1

6mx²+4nxy+2x+2xy-x²+y+4
=6mx²-x²+4nxy+2xy+2x+y+4
=(6m-1)x²+(4n+2)xy+2x+y+4

多项式6mx²+4nxy+2x+2xy-x²+y+4不含二次项
即6m-1=0，4n+2=0
m=1/6
n=-1/2

2m²n+10m-4n+2-2m²n-4m+2n
=2m²n-2m²n+10m-4m-4n+2n+2
=6m-2n+2
=6*1/6-2*(-1/2)+2
=1+1+2
=4

Answer 2

6mx²+4nxy+2x+2xy-x²+y+4
=(6m-1)x²+(4n+2)xy+2x+y+4
∵不含有二次项
∴6m-1=0
4n+2=0
∴m=1/6
n=-1/2
2m²n+10m-4n+2-2m²n-4m+2n
=6m-2n+2
=1+1+2
=4

Answer 3

解：6mx²+4nxy+2x+2xy-x²+y+4＝（6m－1）x2+(4n+2)xy+2x+y+4
不含二次项，有6m-1=0,4n+2=0
解得m＝1/6，n＝－1/2
多项式2m²n+10m-4n+2-2m²n-4m+2n＝6m－2n＋2
当m＝1/6，n＝－1/2时
原式＝6m－2n＋2＝6×1/6－2×（－1/2）＋2＝4

Answer 4

∵关于x,y多项式6mx²+4nxy+2x+2xy-x²+y+4不含二次项

6m=1
4n=-2
∴m=1/6

n=-1/2
∴2m²n+10m-4n+2-2m²n-4m+2n
=6m-2n+2
=1+1+2
=4

Answer 5

6m-1=0,m=1/6,4nxy+2xy=0,n=-1/2,把这两个值代入所求的代数式即可求出值