Question

已知a²-a-1=0,求a^18+32/(a^6)的值,请给出详细解答

Answer 1

a²-a-1=0,求a^18+32(是32，还是323）/(a^6)

追问

题目是别人的，你做过原题？

追答

是

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那感情好，题目应该错了，你按正确题目给答案

追答

a²-a-1=0,求a^18+323/a^6

a^18+323/a^6 =5796

追问

详细解答

追答

a^2-a-1=0
a-1-1/a=0
a-1/a=1 平方
a^2+1/a^2-2=1
a^2+1/a^2=3
a^3-1/a^3=(a-1/a)(a^2+1/a^2+1)
a^3-1/a^3=1*(3+1)
a^3-1/a^3=4 平方
a^6+1/a^6-2=16
a^6+1/a^6=18 平方
a^12+1/a^12+2=324
a^12+1/a^12=322

a^18+323/a^6
=a^18+1/a^6+322/a^6
=a^6*(a^12+1/a^12)+322/a^6
=322*a^6*+322/a^6
=322*(a^6*+1/a^6)
=322*18
=5796