问题
填空题
If the equation m(x-1)=2001-n(x-2)for x has infinite roots,then m2001+n2001=______.(英汉小字典:equation方程;infinite roots无数个根)
答案
m(x-1)=2001-n(x-2),
mx-m=2001-nx+2n,
mx+nx=2001+2n+m,
m+n)x=2001+2n+m,
因为x有无数个根,所以
,m+n=0 2001+2n+m=0
解得:
,m=2001 n=-2001
所以m2001+n2001=20012001+(-2001)2001=0.
故答案为0.