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

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