解题:X+1/X=3,求X²/x⁴+X²+1的值
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解题:X+1/X=3,求X²/x⁴+X²+1的值
解题:X+1/X=3,求X²/x⁴+X²+1的值
解题:X+1/X=3,求X²/x⁴+X²+1的值
X+1/X=3
(X+1/X)² = 9
X²+1/X² +2 = 9
X²+1/X² = 7
X²/x⁴+ X² +1
= X²+1/X² +1
= 8
X+1/X=3
两边同时平方,得
X²+(1/X²)+2=9
X²+(1/X²)=7
X²/(x⁴+X²+1) 分子、分母同时除以X²
=1/[(X²+1+(1/X²)]
=1/(7+1)
=1/8
根据X+1/X=3可以得知X^2-3X+1=0,求解此方程得X=(3加减根号5)/2,将X代入X²/x⁴+X²+1=28加减3根号5
设X²/x⁴+X²+1=s. 1/s=x^2+1/x^2+1 (X+1/X)^2=x^2+1/x^2+2=9 所以 1/s=8. ,s=1/8
(X+1/X)²=X²+1/X²+2=9
X²+1/X²=7
X²/x⁴=1/X²
原式=1/X²+X²+1=8
=1/x^+x^+1
=(1/x+x)^2-1
=9-1
=8