Question

已知a,b,c为三个互不相等的实数,且x/(a-b)=y/(b-c)=z/(c-a),求x+y+z的值.

Answer 1

设 x/(a-b) = y/(b-c) = z/(c-a) = t

则

x + y + z

= (a-b)t + (b-c)t + (c-a)t

=(a-b+b-c+c-a)t

= 0