Question

已知x^2-16x-1=0,求x^2-1/(x^2)的值

Answer 1

x^2-16x-1=0 两边同时除以x得：

x-16-1/x=0 即：x-1/x=16

可得：(x+1/x)^2=(x-1/x)^2+4=260

所以可得：x+1/x=±2√65

x^2-1/(x^2)

=(x+1/x)(x-1/x)

=±32√65