Question

计算：（24+22+1）×（44+42+1）×（64+62+1）×（84+82+1）×（104+102+1）÷（（34+32+1）×（54+52+1

计算：（24+22+1）×（44+42+1）×（64+62+1）×（84+82+1）×（104+102+1）÷（（34+32+1）×（54+52+1）×（74+72+1）×（94+92+1）×（114+112+1））．

Answer 1

∵（x⁴+x²+1）=（x²+x+1）（x²-x+1）；x²-x+1=（x-1）²+（x-1）+1；
∴原式=

(22+2+1)(22?2+1)(42+4+1)(42?4+1)(62+6+1)(62?6+1)(82+8+1)(82?8+1)(102+10+1)(102?10+1)

(32+3+1)(32?3+1)(52+5+1)(52?5+1)(72+7+1)(72?7+1)(92+9+1)(92?9+1)(112+11+1)(112?11+1)

=

(22+2+1)(22?2+1)(42+4+1)(32+3+1)(62+6+1)(52+5+1)(82+8+1)(72+7+1)(102+10+1)(92+9+1)

(32+3+1)(22+2+1)(52+5+1)(42+4+1)(72+7+1)(62+6+1)(92+9+1)(82+8+1)(112+11+1)(102+10+1)

=

22?2+1

112+11+1

=

3

133

．