解cosa^2+cos（α+2π/3）^2+cos（α-2π/3)^2 =(1+cos2a)/2+[cos(2a+4π/3)+1]/2+[cos(2a-4π/3)+1]/2 =(1+cos2a)/2+[1-cos(2a+π/3)]/2+[1-cos(2a-π/3)]/2 =(1+cos2a)/2+1-cos2a/2 =3/2,1,
