Question

(1+根号2)^2001*(1-根号2)^2002的值是

Answer 1

(1+根号2)^2001*(1-根号2)^2002
=(1+根号2)^2001*(1-根号2)^2001*(1-根号2)
=《（1+根号2）（1-根号2）》^2001*(1-根号2)
=（1-2）^2001*(1-根号2)
=-1*(1-根号2)
=根号2-1

Answer 2

(1+√2)^2001*(1-√2)^2002
=(1+√2)^2001*(1-√2)^2001*(1-√2)
=[(1+√2)*(1-√2)]^2001*(1-√2)
=(1-2)^2001*(1-√2)
=-(1-√2)
=√2-1