Question

a²+b²+c²-ab-bc-ca=0,试说明：a=b=c

Answer 1

a²+b²+c²-ab-bc-ca=（2a²+2b²+2c²-2ab-2bc-2ca）/2=（a²+b²-2ab+b²+c²-2bc+a²+c²-2ac）/2=（a-b)^2+(b-c)^2+(a-c)^2=0

（a-b)^2>=0 (b-c)^2>=0 (a-c)^2>=0

所以a=b=c