Question

已知a^2-3a-1=0,求a^3+1/a^3

Answer 1

a²-1=3a
两边除以a
a-1/a=3
两边平方
a²-2+1/a²=9
a²+1/a²=11

(a+1/a)²=a²+2+1/a²=13
a+1/a=±√13

a³+1/a³
=(a+1/a)(a²-a×1/a+1/a²)
=(a+1/a)(a²-1+1/a²)
=±√13(11-1)
=±10√13

Answer 2

很高兴为您解答！答题如下
a平方+3a-1=0
二边同除以a:
a+3-1/a=0
a-1/a=-3
a^2+1/a^2
=a^2+1/a^2 -2+2
=(a-1/a)^2+2
=(-3)^2+2
=11
a^3-1/a^3
=(a-1/a)(a^2+1/a^2+1)
=-3*(11+1)
=-36
希望能帮到您！

Answer 3

a²-3a-1=0
两边除以a:
a-3-1/a=0
a-1/a=3
立方： a³-3a+3/a-1/a³=27
a³-1/a³-3(a-1/a)=27
a³-1/a³-9=27
a³-1/a³=36

Answer 4