Question

如果x满足x²-3x+1=0。那么代数式(x-1/x）²=?

如果x满足x²-3x+1=0。那么代数式(x-1/x）²=?,答案是5，求过程！！！！

Answer 1

将x²-3x+1=0两边同除以X得：x-3+1/x=0
所以x+1/x=3
所以（x+1/x）² =x² +2*x*1/x+1/x² =x² +1/x² +2=9
所以x² +1/x² =7
所以（x-1/x）² =x² -2*x*1/x+1/x² =x² +1/x² -2=7-2=5

Answer 2

(x-1/x）²=x^2+1/x^2-2
x^2=3x-1
原式=3x-1+1/(3x-1)-2=3x-3+1/(3x-1)=[(3x-3)(3x-1)+1]/(3x-1)=[9x^2-12x+4]/(3x-1)
=(9x^2-4x^2)/x^2=5

Answer 3

x²-3x+1=0
两边同除以x得 x+1/x-3=0
则x+1/x=3
两边平方得 x^2+2+1/x^2=9
两边同减去4得
x^2-2+1/x^2=5
左边即为(x-1/x）²
所以(x-1/x）² =5