已知a^2-a-1=0,求a^18 (323/a^6)=?
a^18 (323/a^6)
=(a^2)^9 (323/(a^2)^3)
=(a 1)^9 (323/(a 1)^3)
=A^3 (323/A)
=(A^4 323)/A
其中,A=(a 1)^3
根据已知条件：
a^2-a-1=0
将其化为：(a 1)^2-3(a 1) 1=0
即：(a 1)^2=3(a 1)-1
(a 1)^3=3(a 1)^2-(a 1)=8(a 1)-3
即：A=8(a 1)-3
A^2=64(a 1)^2-48(a 1) 9
=192(a 1)-64-48(a 1) 9
=144(a 1)-55
A^4=20736(a 1)^2-15840(a 1) 3025
=62208(a 1)-20736-15840(a 1) 3025
=46368(a 1)-17711
原式
=(A^4 323)/A
=(46368(a 1)-17711 323)/(8(a 1)-3)
=(46368a 28980)/(8a 5)
=5796*(8a 5)/(8a 5)
=5796
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