Question

√2005×2006×2007×2008+1-2006²怎么算

Answer 1

√(2005×2006×2007×2008+1)-2006²

=√(2005×2008×2006×2007+1)-2006²

=√[2005×(2005+3)×(2005+1)×(2005+2)+1]-2006²

=√[(2005²+3×2005)×(2005²+3×2005+2)+1]-2006²

=√[(2005²+3×2005)²+2×(2005²+3×2005)+1]-2006²

=√[(2005²+3×2005+1)]²-2006²

=(2005²+3×2005+1)-2006²

=2005²+3×2005+1-2006²

=(2005²-2006²)+3×2005+1

=(2005-2006)(2005+2006)+6016

=-4011+6016

=2005