已知a²+3a+1=0,求a³+1/a³和a的四次方+1/a的四次方

已知a²+3a+1=0,求a³+1/a³和a的四次方+1/a的四次方
已知a²+3a+1=0,求a³+1/a³和a的四次方+1/a的四次方

已知a²+3a+1=0,求a³+1/a³和a的四次方+1/a的四次方
a²+3a+1=0
a+1/a=-3
a²+1/a²=7
a³+1/a³
=(a+1/a)(a²-1+1/a²)
=(-3)*[7-1]
=(-3)*6
=-18
a^4+1/a^4
=(a+1/a)(a^3+1/a^3)-a²-1/a²
=(-3)*18-7
=-61