已知y^2+3y-1=0求y^4/y^8+3y^4+1的值
问题描述：
已知y^2+3y-1=0求y^4/y^8+3y^4+1的值
答
答案 1/122
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y^4/(y^8+3y^4+1)
=1/(y^4+3+1/y^4)
=1/[(y^2-1/y^2)^2+5]
=1/[(y+1/y)^2(y-1/y)^2+5]
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y^2+3y-1=0
y=(－3±√13)/2
1/y=(3±√13)/2
y+1/y=±√13 y-1/y=-3
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1/[(y+1/y)^2(y-1/y)^2+5]
=1/(3*3*13+5)=1/122