a²+1/a²=(a^4+1)/a²
=(a²(a²+3a-1)-3a^3+a²+1)/a²
=(a²(a²+3a-1)-3a(a²+3a-1)+9a²-3a+a²+1)/a²
=(a²(a²+3a-1)-3a(a²+3a-1)+11a²-(a²+3a-1))/a²
=(0-0+11a²-0)/a²
=11