问题 填空题
计算
(34+4)(74+4)(114+4)(154+4)…(394+4)
(54+4)(94+4)(134+4)(174+4)…(414+4)
=______.
答案

x4+4=(x2+2)2-(2x)2=(x2+2x+2)(x2-2x+2)=[(x+1)2+1][(x-1)2+1],

∴原式=

(22+1)(42+1)(62+1)(82+1)…(382+1)(402+1)
(42+1)(62+1)(82+1)(102+1)…(402+1)(422+1)
=
22+1
422+1
=
1
353

故答案为:

1
353

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