| R=(2^100-1)x-2^100+2 |
| 送交者: zhf 2020月06月21日08:48:07 於 [靈機一動] 發送悄悄話 |
| 回 答: 修改趣味數學370 由 zhf 於 2020-06-20 12:42:58 |
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x^100/(x^2 - 3x + 2)= x^100/((x-2)(x-1))= x^100(1/(x-2)-1/(x-1)) (1) (x^100-2^100)/(x-2)=q2 x^100/(x-2)=q2+2^100/(x-2) (2) (x^100-1)/(x-1)=q1 x^100/(x-1)=q1 +1/(x-1) (3) (2),(3)代入(1)得 x^100/(x^2 - 3x + 2)=q2-q1+ 2^100/(x-2)-1/(x-1) = q2-q1+ (2^100(x-1)-(x-2))/((x-2)(x-1))= q2-q1+ ((2^100-1)x-2^100+2)/((x-2)(x-1)) R=(2^100-1)x-2^100+2 |
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