a²+1/a²-2a-2/a-6=0
(a+1/a)²-2-2(a+1/a)-6=0
(a+1/a)²-2(a+1/a)-8=0
(a+1/a-4)(a+1/a+2)=0
∴a+1/a=4或a+1/a=-2