若x+1/x=4,则x^2/(x^4+x^2+1)=
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若x+1/x=4,则x^2/(x^4+x^2+1)=
若x+1/x=4,则x^2/(x^4+x^2+1)=
若x+1/x=4,则x^2/(x^4+x^2+1)=
x+1/x=3,两边平方,
x^2+1/x^2+2=9
x^2+1/x^2=7
(x^4+x^2+1)/x^2=x^2+1+1/x^2=7+1=8
x^2/(x^4+x^2+1) = 1 / [(x^4+x^2+1)/x^2] = 1/8
若x+(1/x)=4,则x²/(x⁴+x²+1)=?
由x+(1/x)=4,平方得x²+(1/x²)+2=16,即x²+(1/x²)=14;
故x²/(x⁴+x²+1)=1/[x²+(1/x²)+1]=1/(14+1)=1/15.
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