Question

(x)1/m = (y)1/n = (z)1/p and xyz = 1. What is the value of m+n+p?

Answer 1

xyz = y^(m/n) * y * y^(p/n) = 1
which gives,
y^(m/n + 1 + p/n) = 1
But if y^k = 1, then k = 0!
So,
(m/n + 1 + p/n) = 0
m/n + n/n + p/n = 0
(m+n+p)/n = 0
m+n+p = 0