a^2-1/a^2=2(a-1/a),
(a-1/a)(a+1/a)-2(a-1/a)=0,
(a-1/a)(a+1/a-2)=0,
[(a^2-1)]/a*[(a-1)^2/a]=0,
(a+1)(a-1)^3/a^2=0,
a=±1.