Question

$if {a}^x = {b}^y = {c}^z \: show \: that \: \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$
solve it please​

Answer 1

Step-by-step explanation:

Let a^x = b^y = c^z = abc = k

a^x = k => a = k^ (1/x). Similarly, b = k^(1/y) and c = k^(1/z)

Now abc = k

=> k^(1/x) k^(1/y)k^(1/z) = k

=> k^{(1/x + 1/y + 1/ z)} = k^1

Since the bases are same we can equate the indices.

Hence we get 1/x + 1/y + 1/z = 1.