similarly b=(abc)^\frac{1}{y}\cdots(2)
c=(abc)^\frac{1}{z}\cdots(3)
multiplying (1) (2) and (3) we get abc = (abc)^{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}
or
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1
multiplying both sides by xyz we get the result