Question

已知x^2-5x/2+1=0，求x^2+1/x及x-1/x的值。帮我啊！

Answer 1

已知x^2-5x/2+1=0，求x^2+1/x及x-1/x的值。

x^2-5x/2+1=0
2x^2-5x+2=0
(2x-1)(x-2)=0
x1=1/2
x2=2

x1=1/2
x^2+1/x=1/4+2=9/4
x-1/x=1/2-2=-3/2

x2=2
x^2+1/x=4+1/2=9/2
x-1/x=2-1/2=3/2

Answer 2

x^2-5x/2+1=0

x+1/x=5/2
所以
x²+1/x²=(x+1/x)²-2=17/4
(x-1/x)²=(x+1/x)²-4=9/4
x-1/x=±3/2

Answer 3

(x-5/4)^2=9/16
x-5/4=3/4或者-3/4
x=2或1/2
当x=2时，x^2+1/x=9/2, x-1/x=3/2
当x=1/2是，x^2+1/x=9/4, x-1/x=-3/2

Answer 4

x^2-5x+1=0,
x-5+1/x=0
x+1/x=5
x^2+1/x^2=(x+1/x)^2-2=5^2-2=25-2=23