已知:A是实数,且a^2+a-1=0,求a^5-5a-3

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已知:A是实数,且a^2+a-1=0,求a^5-5a-3

已知:A是实数,且a^2+a-1=0,求a^5-5a-3
已知:A是实数,且a^2+a-1=0,求a^5-5a-3

已知:A是实数,且a^2+a-1=0,求a^5-5a-3
∵a^2+a-1=0
∴a^2+a=1
a^2=1-a
∴a^5-5a-3
=a(1-a)²-5a-3
=a(1-2a+a²)-5a-3
=a(1-2a+1-a)-5a-3
=2a-3a²-5a-3
=-3(a²+a)-3
=-3-3
=-6

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然后得出两个结果

a^5-5a+3
=a³﹙a²+a-1﹚-a^4+a³-5a+3
=a³﹙a²+a-1﹚-a²﹙a²+a-1﹚+2a³-a²-5a+3
=2a﹙a²+a-1﹚-3a²-3a+3
=-3﹙a²+a-1﹚
=0
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a^5-5a+3
=a³﹙a²+a-1﹚-a^4+a³-5a+3
=a³﹙a²+a-1﹚-a²﹙a²+a-1﹚+2a³-a²-5a+3
=2a﹙a²+a-1﹚-3a²-3a+3
=-3﹙a²+a-1﹚
=0
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