已知a²=a+1,求代数式a^5-5a+2的值

已知a²=a+1,求代数式a^5-5a+2的值
已知a²=a+1,求代数式a^5-5a+2的值

已知a²=a+1,求代数式a^5-5a+2的值
a^5-5a+2=a³×a²-5a+2
=a³(a+1)-5a+2
=a^4+a³-5a+2
=(a²)²+a×a²-5a+2
=(a+1)²+a(a+1)-5a+2
=a²+2a+1+a²+a-5a+2
=2a²-2a+3
=2(a+1)-2a+3
=2a+2-2a+3
=5
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