化简:(根号下“x+2乘以根号下x+1”)+(根号下“x-2乘以根号下x-1”)化简:(根号下“x+2乘以根号下x-1”)+(根号下“x-2乘以根号下x-1”)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 06:07:48

化简:(根号下“x+2乘以根号下x+1”)+(根号下“x-2乘以根号下x-1”)化简:(根号下“x+2乘以根号下x-1”)+(根号下“x-2乘以根号下x-1”)
化简:(根号下“x+2乘以根号下x+1”)+(根号下“x-2乘以根号下x-1”)
化简:(根号下“x+2乘以根号下x-1”)+(根号下“x-2乘以根号下x-1”)

化简:(根号下“x+2乘以根号下x+1”)+(根号下“x-2乘以根号下x-1”)化简:(根号下“x+2乘以根号下x-1”)+(根号下“x-2乘以根号下x-1”)
X= 负的根号下2

解析:
原式=√[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│
当1≤x≤2时,原式=√(x-1)+1+√(x-1)-1=2√(x-1),
当x>2时,原式=√(x-1)+1-√(x-1)+1=2