# 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