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已知y²+3y-1=0,(y^4)/(y^8-3y^4+1)的值.
题目详情
已知y²+3y-1=0,(y^4)/ (y^8-3y^4+1)的值.
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答案和解析
y^2+3y-1=0
y+3-1/y=0
y-1/y=-3
(y-1/y)^2=9
y^2+1/y^2-2=9
y^2+1/y^2=11
(y^2+1/y^2)^2=121
y^4+1/y^4+2=121
y^4+1/y^4=119
y^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
y+3-1/y=0
y-1/y=-3
(y-1/y)^2=9
y^2+1/y^2-2=9
y^2+1/y^2=11
(y^2+1/y^2)^2=121
y^4+1/y^4+2=121
y^4+1/y^4=119
y^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
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