Question

若x的平方-根号2X-1=0,则X-1/X=根号2

Answer 1

x^2-√(2x-1)=0

x^4=2x-1

x^4-2x+1=0

若x-(1/x)=√2

则

(x^2-1)^2=2x^2

x^4+1-2x^2=2x^2

x^4-4x^2+1=0

2x-4x^2=0

x(1-2x)=0

x=0,x=1/2

因为x≠0

所以是假命题