If the equation m(x-1)-n(x-2)for x has infinite roots,then m(的2005次方)+n(的2005次方)=
来源:百度知道 编辑:UC知道 时间:2024/05/25 10:04:14
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If the equation m(x-1)-2005-n(x-2)for x has infinite roots,then m(的2005次方)+n(的2005次方)=
If the equation m(x-1)-2005-n(x-2)for x has infinite roots,then m(的2005次方)+n(的2005次方)=
m^(x-1)-n^(x-2)=0
→
① if m=n=0,
m(的2005次方)+n(的2005次方)=0;
② if m=n=1,
m(的2005次方)+n(的2005次方)=2;
③ others:
m^(x-1)-n^(x-2)=0 →m-(n/m)^(x-2)=0 →(n/m)^(x-2)=m;
in the case of n>m>0,
→{
lim(x→-∞) (n/m)^(x-2)=0=m, error;
lim(x→+∞) (n/m)^(x-2)=+∞=m, error;
in the case of m>n>0,
lim(x→-∞) (n/m)^(x-2)=+∞=m, error;
lim(x→+∞) (n/m)^(x-2)=0=m, error;
so
m(的2005次方)+n(的2005次方)=0 or 2.
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