Question

已知x=-7+4根号3,y=-7-4根号3,求根号y/x-根号x/y

Answer 1

y/x

=(-7-4√3)/(-7+4√3)

上下同乘(-7-4√3)

=(-7-4√3)^2/(49-16*3)

=(-7-4√3)^2/1

=(-7-4√3)^2

x/y

=(-7+4√3)/(-7-4√3)

上下同乘(-7+4√3)

=(-7+4√3)^2/(49-16*3)

=(-7+4√3)^2

∴

√(y/x)-√(x/y)

=√(-7-4√3)^2-√(-7+4√3)^2

=7+4√3-(7-4√3)

=7+4√3-7+4√3

=8√3