If #1/(x^b+x^(-c)+1) + 1/(x^c+x^-a+1) + 1/(x^a+x^(-b)+1) = 1# then what can we say about #a, b, c# ?
2 Answers
Explanation:
For any non-zero value of
So with
#1/(x^b+x^(-c)+1) + 1/(x^c+x^-a+1) + 1/(x^a+x^(-b)+1)#
#=1/3+1/3+1/3 = 1#
Actually as seen in https://socratic.org/s/axdYQgwe, if
Note also that if
#1 = 1/(x^k+x^(-k)+1) + 1/(x^k+x^-k+1) + 1/(x^k+x^(-k)+1)#
#=3/(x^k+x^(-k)+1)#
So we have:
#x^k+x^(-k)+1 = 3#
Subtracting
#0 = (x^k)^2-2(x^k)+1 = (x^k-1)^2#
So
This is satisfied for any non-zero value of
Explanation:
Using "brute force" or with the help of a symbolic processor,
but
Solving for