Question

x²-5x-1=0求x²+x²分之一

Answer 1

x²-5x-1=0
x²-1=5x 两边除以x
x-1/x=5
（x-1/x）²=5²
x²-2+1/x²=25
x²+1/x²=27

追问

谢谢，明白了

Answer 2

x²-5x-1=0，显然x≠0
所以两边除以x得到：x-5-(1/x)=0
==> x-(1/x)=5
==> [x-(1/x)]²=5²=25
==> x²-2+(1/x²)=25
==> x²+(1/x²)=27