Question

lg((31+10√6)^12+(31-10√6)^12)

Answer 1

   $lg(sqrt{31+10sqrt6}+sqrt{31-10sqrt6})=lg(sqrt{(5+sqrt6)^2}+sqrt{(5-sqrt6)^2})=\\=lg(|5+sqrt6|+|5-sqrt6|)=lg(5+sqrt6+5-sqrt6)=lg10=1$