a+b+c=1所以a=1-b-c,代入a^2+b^2+c^2=1,得(1-b-c)^2+b^2+c^2=1,整理得2b^2+2(c-1)b+2c^2-2c=0,b,c为实数，<==>△/4=(c-1)^2-2(2c^2-2c)=-3c^2+2c+1=-3(c-1)(c+1/3)≥0,解得-1/3≤c≤1.
