一条初一代数式题已知a^2=a+1,求代数式a^5 - 知识问答

一条初一代数式题已知a^2=a+1,求代数式a^5-5a+2

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∵a^2=a+1
∴用a+1来代替a^2以达到降次的目的
a^5-5a+2
=a^2*a^2*a-5a+2
=(a+1)*(a+1)*a-5a+2
=(a^2+2a+1)*a-5a+2
=(a+1+2a+1)*a-5a+2
=(3a+2)*a-5a+2
=3a^2+2a-5a+2
=3(a+1)+2a-5a+2
=3a+3+2a-5a+2
=5

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