若x,y为实数,且y=√(x^2-4)+√(4-x^2)+1/(x+2),求√（x+y）÷√（x-y）的值这是我明天要交的作业中的题,今天没答案就完蛋了,希望各位老师帮我解决!（sorry,quickly.

Question

若x,y为实数,且y=√(x^2-4)+√(4-x^2)+1/(x+2),求√（x+y）÷√（x-y）的值
这是我明天要交的作业中的题,今天没答案就完蛋了,希望各位老师帮我解决!（sorry,
quickly.

Answer 1

x,y为实数,且
y=√(x^2-4)+√(4-x^2)+1/(x+2)
等式有意义需x^2-4≥0且4-x^2≥0,x+2≠0
所以x^2-4=0,x≠-2
x^2=4,x≠-2
那么x=2
∴ y=1/(2+2)=1/4
∴√(x+y)÷√(x-y)
=√(2+1/4)÷√(2-1/4)
=√(9/4)÷√(7/4)
=3/√7
=3√7/7