Question

If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0

Answer 1

Let `root(x)("a") = root(y)("b") = root(z)("c")` 

⇒ `"a"^(1/x) = "k", "b"^(1/y) = "k", "c"^(1/z) = "k"`
⇒ a = k, b = k, c = k
It is also given that abc = 1
⇒  k^x x k^y x k^z = 1
⇒  `"k"^(x + y + z)` = k^°
⇒  x + y + z = 0.