Question

关于x,y的多项式6mx²+4nxy+2x+2xy-x²+y+4不含二次项，

求多项式2m²n+10m-4n2+2m²n+4m+2n的值

Answer 1

6mx²+4nxy+2x+2xy-x²+y+4
=(6m-1)x²+(4n+2)xy+2x+y+4
6m-1=0
m=1/6
4n+2=0
n=-1/2

2m²n+10m-4n2+2m²n+4m+2n
=4m²+14m-4n²+2n
=4x(1/6)²+14x1/6-4x(-1/2)²-2x1/2
=1/9+7/3-1-1
=1/9+1/3
=4/9

追问

题抄错了-_-。sorry！
是2m²n+10m-4n+2-2m²n-4m+2n

追答

2m²n+10m-4n+2-2m²n-4m+2n
=6m-2n+2
=6x1/6+2x1/2+2
=1+1+2
=4

追问

不对吧？

追答

对的

Answer 2

6mx²+4nxy+2x+2xy-x²+y+4
=(6m-1)x²+(4n+2)xy+2x+y+4 不含二次项，则 6m-1=0，4n+2=0
m=1/6，n= -1/2
2m²n+10m-4n2+2m²n+4m+2n
=4m²n+14m-4n^2+2n
=2m(2mn+7)-2n(2n-1)
=5/18

Answer 3

解：由题可知
6mx²+4nxy+2x+2xy-x²+y+4=(6m-1)x²+(4n+2)xy+2x+y+4
即6m-1=0,4n+2=0 可得 m=1/6,n=-1/2
所以代入2m²n+10m-4n2+2m²n+4m+2n可得其值