Question: Calculate when something is real

Hi there.

 

I have two vectors:

x1:= [ ( 1+sqrt(1-4*a^2) )/(2*a) , ( 1+sqrt(1-4*a^2) )/2 ];

x2:= [ ( 1-sqrt(1-4*a^2) )/(2*a) , ( 1-sqrt(1-4*a^2) )/2 ];

I have the following questions to complete:

(2)Determine when x1 and x2 are both real

(3)Determine the largest interval I=(c,d) (with d>0) such that x1 and x2 are real and distinct.

 

The answers are obvious on paper, but I have to calculate this with Maple.  How do I go about this?

 

Thanks

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