(√6+1)^2014-2(√6+1)^2013-5(√6+1)^2012+2013
=(√6+1)^2012 ×[(√6+1)²-2(√6+1)-5]+2013
=(√6+1)^2012 ×[(√6+1)(√6-1)-5]+2013
=(√6+1)^2012 ×0+2013
=2013