(1)化简:;(2)已知4x2-4x-15≤0,化简;+(3)化简:.+-

(1)化简:

(2)已知4x2-4x-15≤0,化简;+

(3)化简:.+-

答案

解析:对(1),被开方数是一个完全平方式,根据根式的运算性质求解;对(2),先根据条件“4x2-4x-15≤0”求出x的范围,再化简求值;对(3),要注意观察被开方数是哪个数的平方,然后根据根式的性质化简.

解:(1)

==|x+y|=

 (2)∵4x2-4x-15≤0,∴-

≤x≤.∴2x+3≥0,2x-5≤0.

=

=2x+3-2x+5=8.

(3)

=

=

-+2--2+=0.

深化升华

(1)此组题目均是考查

=|a|(n为偶数)这一公式的应用,要注意被开方式的符号.

(2)对有限制条件的根式化简问题,其解决方法是:先求出条件对字母的限制范围,在些范围内,根据根式的意义、性质进行化简.如果没有限制条件,则应分类讨论.如本例(2)中去掉限制条件,则应分x<-

,-≤x≤,x>三种情况讨论.

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