已知X=(√5-1)/2,求(x³﹢x+1)/x的5次方的值?

2025-05-10 07:31:48
推荐回答(2个)
回答1:

X=(√5-1)/2 (1)
平方x^2=(6-2√5)/4
2x^2=3-√5
√5=3-2x^2
代入(1) x=1-x^2
x^2=1-x
所以(x³﹢x+1)/x的5次方=(x-x^2+x+1)/x^5
=(2x+1-x^2)/x^5=3x/x^5=3/x^4=3/(1-x)^2=3/(1-2x+x^2)=3/(2-3x)
=3/[2-3(√5-1)/2]=6/(7-3√5)=3(7+3√5)/2

回答2:

X=(√5-1)/2 (1)
平方x^2=(3-√5)/2
1/x==(√5+1)/2
(x³﹢x+1)/x
=x2+1+1/x
=3
所以(x³﹢x+1)/x的5次方
=3 的5次方
=243