已知0<x<1,化简根号下(x-1/x)²+4-根号下(x+1/x)²-4

Question

如题所述

Answer 1

∵0<x<1
∴x<1/x
√[(x-1/x)^2+4]-√[(x+1/x)^2-4]
=√[(x^2-2+1/x^2)+4]-√[(x^2+2+1/x^2)-4]
=√(x+1/x)^2-√(x-1/x)^2
=x+1/x-(1/x-x)
=2x