Question

How many real roots does the equation (x-a)^3+(x-b)^3+(x-c)^3=0 have, if a,b,c are real numbers such that a,b,c are not all equal.

Answer 1

expand it for starters and lets see if we can draw some conclusions for first and 2nd derivatives

Answer 2

A quick graphical look seems to suggest only 1 root. But I haven't done any anaysis

Answer 3

i suppose we can do it without expanding too i guess