已知a²-3a+1=0,求a³/a^6+a³+1的值
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已知a²-3a+1=0,求a³/a^6+a³+1的值
已知a²-3a+1=0,求a³/a^6+a³+1的值
已知a²-3a+1=0,求a³/a^6+a³+1的值
a²-3a+1=0
a-3+1/a=0
a+1/a=3
a^3+1/a^3=(a+1/a)(a^2-1+1/a^2)
a^3+1/a^3=(a+1/a)[(a^2+2+1/a^2)-3]
a^3+1/a^3=(a+1/a)[(a+1/a)^2-3]
a^3+1/a^3=3*(3^2-3)
a^3+1/a^3=18
a^3+1/a^3+1=19
(a^6+a^3+1)/a^3=19 取倒数
a^3/(a^6+a^3+1)=1/19