y^+3y-1=0,求y^4/^8-3y^4+1的值
问题描述：
y^+3y-1=0,求y^4/^8-3y^4+1的值
答
y^2+3y-1=0y+3-1/y=0y-1/y=-3(y-1/y)^2=9y^2+1/y^2-2=9y^2+1/y^2=11(y^2+1/y^2)^2=121y^4+1/y^4+2=121y^4+1/y^4=119y^4/(y^8-3y^4+1)=1/(y^4-3+1/y^4)=1/(y^4+1/y^4-3)=1/(119-3)=1/116