Question

已知x=(根号5+1)/2求x三次方/x三次方+x+1

Answer 1

x-1/2=根5/2
2x-1=根5
4x^2-4x+1=5
x^2=x+1

x^3/(x^3+x+1)=x^3/(x^3+x^2)=x/(x+1)=((根号5+1)/2)/(=(根号5+1)/2+1)=(根号5+1)/(根号5+3)
=(根号5+1)(根号5-3)/(5-3^2)=(5-2根5-3）/（-4）
=（根5-1）/2

追问

x^3/(x^3+x+1)怎么会等于x^3/(x^3+x^2)？

追答

上面不是算了吗，x^2=x+1,x+1=x^2代入分母就可以得到

Answer 2

已知x=(根号5+1)/2
2x-1=根号5
平方得 4x²-4x+1=5
即x²=x+1
所以x三次方/(x三次方+x+1)
=x(x+1)/[x(x+1)+x+1]
=x/(x+1)
=1/(1+1/x)
=1/[1+2/(√5+1)]
=(√5+1)/(3+√5)
=(1+√5)(3-√5)/(9-5)
=(2√5-2)/4
=(√5-1)/2

Answer 3

X直接就可以算啊。。。
X=（根号5+1）立方/8=（16+8*根号5)/8=2+根号5