SOLUTION: X^1/m=Y^1/n=Z^1/p, xyz=1 then m+n+p=?

Question 42061: X^1/m=Y^1/n=Z^1/p, xyz=1 then m+n+p=?
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
You have,
x^(1/m)=y^(1/n)=z^(1/p)
From,
x^(1/m)=y^(1/n)
x = y^(m/n) -------------(1)
===========
From,
y^(1/n)=z^(1/p)
z = y^(p/n) -------------(2)
===========
Using (1) and (2),
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
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