若 ,X^2-5X-1=0,求分式X^2/(X^4+X^2+1 )的值.
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若,X^2-5X-1=0,求分式X^2/(X^4+X^2+1)的值.若,X^2-5X-1=0,求分式X^2/(X^4+X^2+1)的值.若,X^2-5X-1=0,求分式X^2/(X^4+X^2+1)的
若 ,X^2-5X-1=0,求分式X^2/(X^4+X^2+1 )的值.
若 ,X^2-5X-1=0,求分式X^2/(X^4+X^2+1 )的值.
若 ,X^2-5X-1=0,求分式X^2/(X^4+X^2+1 )的值.
x^2-5x-1=0
x^2-1=5x
(x^2-1)^2=25x^2
x^4-2x^2+1=25x^2
x^4-2x^2+1+3x^2=25x^2+3x^2
x^4+x^2+1=28x^2
x^2/(x^4+x^2+1)=1/28
x^2-5x-1=0
x^2-1=5x 除x
x-1/x=5 平方
x^2-2+1/x^2=25
x^2+1/x^2=27
X^2/(X^4+X^2+1 ) 分子分母除x^2
1/(x^2+1+1/x^2)
=1/(27+1)
=1/28
由X^2-5X-1=0得,(x-5/2)^2-25/4-1=0,从而求得x=5/2+(-)根号29/2。再将x带入即可
X^2-5X-1=0,
x-5-1/x=0
x-1/x=5
(x-1/x)^2=25
x^2+1/x^2=27
X^2/(X^4+X^2+1 )
=1/(x^2+1+1/x^2)
=1/(27+1)
=1/28
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