已知a²+3a+1=0,求(1)a+1/a(2)a²+1/a²(3)a四次方+1/a四次方
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已知a²+3a+1=0,求(1)a+1/a(2)a²+1/a²(3)a四次方+1/a四次方
已知a²+3a+1=0,求(1)a+1/a(2)a²+1/a²(3)a四次方+1/a四次方
已知a²+3a+1=0,求(1)a+1/a(2)a²+1/a²(3)a四次方+1/a四次方
a^2-3a+1=0,
二边同除以:a
a-3+1/a=0
(1)
a+1/a=3
(2)
a^2+1/a^2
=(a+1/a)^2-2
=3^2-2
=7
(3)
a^4+1/a^4
=(a^2+1/a^2)^2-2
=7^2-2
=49-2
=47
(1)∵a²+3a+1=0
∴a+3+1/a=0
a+1/a=-3
(2) (a+1/a)²=9
a²+2+1/a²=9
a²+1/a²=7
(3) (a²+1/a²)²=49
a⁴+2+1/a⁴=49
a⁴+1/a⁴=47