若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.

若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.
若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.

若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.
(a+1/a)^2=a^2+2a*1/a+1/a^2=a^2+2+1/a^2
所以a^2+1/a^2=(a+1/a)^2-2
a^2+5a-4+5/a+1/a^2=0
(a+1/a)^2-2+5(a+1/a)-4=0
令x=a+1/a
则x^2+5x-6=0
(x-1)(x+6)=0
x=1,x=-6
若x=a+1/a=1
则a^2+1=a
a^2-a+1=0,此方程无解
所以a+1/a=x=-6

a^2+5a-4+5/a+1/a^2=(a^2+1/a^2+2)+5(a+1/a)-6
=(a+1/a)^2+5(a+1/a)-6=0
a+1/a=1或-6