因为1≤x≤2
所以0≤x-1≤1
所以0≤√(x-1)≤1
√[x+2√(x-1)]-√[x-2√(x-1)]
=√[(x-1)+2√(x-1)+1]-√[(x-1)-2√(x-1)+1]
=√[√(x-1)+1]²-√[√(x-1)-1]²
=|√(x-1)+1|-|√(x-1)-1|
=(√(x-1)+1)-(1-√(x-1))
=√(x-1)+1-1+√(x-1)
=2√(x-1)