解方程:y^2+1/y^2+2y+(2-6y)/y=0

题目

解方程:y^2+1/y^2+2y+(2-6y)/y=0
高手想想办法...

答案

y^2+1/y^2+2y+(2-6y)/y=0 (y+1/y)^2-2+2y+2/y-6=0设y+1/y=t.t^2+2t-8=0(t+4)(t-2)=0t1=-4,t2=2(1)t=-4y+1/y=-4y^2+4y+1=0(y+2)^2=3y1=-2+根号3y2=-2-根号3(2)t=2:y+1/y=2y^2-2y+1=0y=1即有以上三个解.