已知x+1/x=3,求x^2+1/x^2 x^2+1/x^2=(x+1/x)^2-2=9-2=7 (2)借鉴上题的解法求解已知x^2-5x+1=0 求x-1/x

已知x+1/x=3,求x^2+1/x^2 x^2+1/x^2=(x+1/x)^2-2=9-2=7 (2)借鉴上题的解法求解
已知x^2-5x+1=0 求x-1/x

x^2-5x+1=0
x-5+1/x=0
x+1/x=5
（x+1/x）²=25
x²+2+1/x²=25
x²-2+1/x²=21
（x-1/x）²=21
x-1/x = ±√21