a^3+3a^2+a=0 5a^2/a^4+8a^2+1=?
1个回答

a^3+3a^2+a=0,得:a=0或a^2+3a+1=0,即a^2=-1-3a.

所以:5a^2/(a^4+8a^2+1)= 0 或1/3. 0很容易理解,下面是1/3的推导过程:

把a^2=-1-3a带入式子:

5a^2/(a^4+8a^2+1)=(-5-15a)/(a^4+8a^2+1)= (-5-15a)/((-5-15a)^2+8(-5-15a)+1 )= (-5-15a)/(-45a-15)= 1/3