(In reply to
Partial(?) solution by tomarken)
Consider a polynom p= x^3+x^2-1
p=0 has
at most 3 solutions, distinct or equal, call them a, b, c - so:
0=(x-a)*(x-b)*(x-c) therefore AT LEAST ONE IS TRUE:
(x-a)=0 OR
(x-b)=0 OR
(x-c)=0
Easy to show that a=b implies a=c (by substitution )
and since NO 4th ANSWER IS POSSIBLE
We conclude that (a-b)(b-c)(c-a) = 0.
No need to solve the equation!
Edited on February 20, 2020, 5:59 am
re: Partial(?) solution
