(a²-b²+2)/2 -(a²-2b²+1)/3 =(3a²-3b²+6)/6 - (2a²-4b²+2)/6
=(3a²-3b²+6 - 2a²+4b²-2)/6 =(a²+b²+4)/6>=4/6>0
即:(a²-b²+2)/2 -(a²-2b²+1)/3 >0
所以:(a²-b²+2)/2 >(a²-2b²+1)/3
(a²-b²+2)/2 -(a²-2b²+1)/3 =(3a²-3b²+6)/6 - (2a²-4b²+2)/6
=(3a²-3b²+6 - 2a²+4b²-2)/6 =(a²+b²+4)/6>=4/6>0
即:(a²-b²+2)/2 -(a²-2b²+1)/3 >0
所以:(a²-b²+2)/2 >(a²-2b²+1)/3