Question

已知x的平方-3x+1=0，试求下列各式的值 x的立方+x的立方分之一

方程，步骤，急！！！

Answer 1

解:∵X²-3X+1=0,则X≠0.
∴方程两边同除以X,得:X-3+1/X=0, X+1/X=3;

则(X+1/X)²=9, X²+1/X²+2=9, X²+1/X²=7.
故X³+1/X³=(X+1/X)(X²+1/X²)-(X+1/X)=3*7-3=18.

Answer 2

x^2=3x-1
x^3=3x^2-x=3*(3x-1)-x=8x-3
x的立方+x的立方分之一=8x-3+8x-3分之一=8x-3分之(8x-3)^2+1=8x-3分之64x^2-48x+10=8x-3分之64(3x-1)-48x+10=8x-3分之144x-54=18

Answer 3

x^2-3x+1=0
即x-3+1/x=0
x+1/x=3
所以x^3+1/(x^3)
=(x+1/x)^3-3(x+1/x)
=3^3-3*3
=18

这里用到公式a^3+b^3=(a+b)^3-3ab(a+b)

Answer 4

x^2+1=3x
x+1/x=3
(x+1/x)^2=3^2
x^2+2+1/x^2=9
x^2+1/x^2=7

(x^3+1/x^3)
=(x+1/x)(x^2-1+1/x^2)
=3(9-1)
=24