数学题:已知a^2 + 4a + 1 =0,且(a^4 + ma^2 +1)⼀(3a^3 + ma^2 + 3a)=5,则m=( )

2025-02-01 01:01:23
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回答1:

a^2+1=-4a so, a^4+2a^2+1=16a^2 so, a^4+1=14a^2
a^4+ma^2+1=(14+m)a^2
3a^3+ma^2+3a=3a(a^2+ma/3+1)=3a*(ma/3-4a)=(m-12)a^2
(a^4+ma^2+1)/(3a^3+ma^2+3a)=(14+m)/(m-12)=5
m=37/2