高手pufa 回覆於: 2004/9/24 上午 12:38:45
P(z)=200z^5+201z^4+202z^3+203z^2+204z+205=0
P(1)>0;z not=1
P(z)*(z-1)=(200*z^6+z^5+z^4+z^3+z^2+z)-205=0
200*z^6+z^5+z^4+z^3+z^2+z=205
1>=|z|; z not=1
=> 1>=|z^6|; 1>=|z^5|,..., 1>=|z|
205=200+1+1+1+1+1>=200*|z^6|+|z^5|+|z^4|+|z^3|+|z^2|+|z|
>=|200*z^6+z^5+z^4+z^3+z^2+z|=205
so, z^6=z^5=z^4=z^3=z^2=z=1
but z not=1
so, P(z)=0在{z屬於C,1>=|z|}中,沒有任何解.