Make a discovery?

Question

show that the polynomial
(a-b)^(n)+nk(a-b)=1
has no real solutions for a , b & k if n>2.
if n=2 then for e.g.
a=1.25 , b=0.75 & k = 0.75

Answer 1

unfortunately you are mistaken.

we can rearrange taking a != b

nk(a-b) = 1-(a-b)^n
or k = (1-(a-b)^n)/n(a-b)

for any a and a and b we can compute k k shall be rational if and b are

with regards

Answer 2

But it does, unless I am missing something: if k = 0 and a = 1 + b it is true for any value of n.