SOLUTION: a = 2+ sqare root of 3. to find a^2 +1/a^2

First let us prove this statement:


    If a = , then  = 


Indeed,   =  = 4 - 3 = 1,  so the statement is proved.


Next,   +  = .   (*)


Notice that   =  +  = 4.


Therefore, we can continue (*) in this way:


 +  =  =  = 16 - 2 = 14.


Answer.  If  a =   then   = 14.