Question

实数a,b,c满足a^2+b^2+c^x=667,则代数式(a-b)^2+(b-c)^2+(c-a)^2的最大值是

Answer 1

(a-b)^2+(b-c)^2+(c-a)^2

=a^2+b^2+b^2+c^2+c^2+a^2-(2ab+2bc+2ac)

=2*667-(2ab+2bc+2ac)

又a^2+b^2>=2ab;

b^2+c^2>=2bc;

c^2+a^2>=2ac;

所以2ab+2bc+2ac