Question

已知a=根号2+1,求a的三次方-a的平 方-3a+2013的值

Answer 1

解由a=√2+1
即a^2=3+2√2
故a^3-a^2-3a+2013
=a(a^2-a-3)+2013
=a(3+2√2-（√2+1）-3）+2013
=a(3+2√2-√2-1-3）+2013
=(√2+1)(√2-1）+2013
=1+2013
=2014