Question

M=2010²+2010²×2011²+2011²,求M的平方根?

Answer 1

M=2010²+2010²×2011²+2011²

设a=2010

则M=a^2+a^2(a+1)^2+(a+1)^2

=a^2+(a^2+1)(a+1)^2

=a^2+(a^2+1)(a^2+1+2a)

=a^2+(a^2+1)^2+2a(a^2+1)

=(a^2+1)^2+2a(a^2+1)+a^2

=(a^2+a+1)^2

所以M的平方根=正负(a^2+a+1)=正负4 042 111