Question

已知x+x的负一次=3,求x的平方减x的负二次方等于多少

Answer 1

x+1/x=3

(x+1/x)^2=9

x^2+1/x^2+2=9

x^2+1/x^2=7

x^2+1/x^2-2=7-2

(x-1/x)^2=5

x-1/x=±√5

x^2-1/x^2

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

=3*√5

=3√5

或

x^2-1/x^2

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

=3*(-√5)

=-3√5