Question

若1〈=x〈=2时化简 x+2√x—1的算术平方根减去x—2√x—1的算术平方根（过程

Answer 1

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)