题目不错：
令b=(cost,sint)
|an+b|^2=|an|^2+|b|^2+2an·b
=2+2(cos(nπ/7),sin(nπ/7))·(cost,sint)
=2+2[cos(nπ/7)cost+sin(nπ/7)sint]
故：y=2+2[cos(π/7)cost+sin(π/7)sint]+2+2[cos(2π/7)cost+sin(2π/7)sint]+...
+2+2[cos(141π/7)cost+sin(141π/7)sint]
=2*141+2cost(cos(π/7)+cos(2π/7)+...+cos(141π/7))
+2sint(sin(π/7)+sin(2π/7)+...+sin(141π/7))
cos(π/7)+cos(2π/7)+...+cos(14π/7)=cosπ+cos2π=0
故：cos(π/7)+cos(2π/7)+...+cos(141π/7)=cos(π/7)
sin(π/7)+sin(2π/7)+...+sin(14π/7)=sinπ+sin2π=0
故：sin(π/7)+sin(2π/7)+...+sin(141π/7)=sin(π/7)
故：y=282+2costcos(π/7)+2sintsin(π/7)
=282+2cos(t-π/7)
故y的最大值：284