4x²+kxy+y²=（2x+2y+3^1/2)(mx+ny)=2mx^2+2nxy+2mxy+2ny^2+3^1/2mx+3^1/2ny
=2mx^2+(2n+2m)xy+2ny^2+3^1/2mx+3^1/2ny
2m=4 (2n+2m)=k 2n=1 3^1/2m=0 3^1/2n=0
m、n、k无解,题目有误
可能是4x²+kxy+y²=（2x+2y)(mx+ny)
4x²+kxy+y²=（2x+2y)(mx+ny)=2mx^2+(2n+2m)xy+2ny^2
2m=4 (2n+2m)=k 2n=1
m=2 n=1/2 k=5