若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.
问题描述：
若a^2+5a-4+5/a+1/a^2=0,求a+1/a的值.
答
(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)^2-2a^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)=0x=1,x=-6若x=a+1/a=1则a^2+1=aa^2-a+1=0,此方程无解所以a+1/a=x=...