Answer: see proof below
Step-by-step explanation:
[tex]x^a=y^b=z^c\ =k\\[/tex]
Then [tex]x^a=k\qquad \rightarrow \qquad x=k^{\frac{1}{a}}[/tex]
and [tex]y^b=k\qquad \rightarrow \qquad y=k^{\frac{1}{b}}[/tex]
and [tex]z^c=k\qquad \rightarrow \qquad z=k^{\frac{1}{c}}[/tex]
y³ = x · z
[tex](k^{\frac{1}{b}})^3=k^{\frac{1}{a}}\cdot k^{\frac{1}{c}}\\\\k^\frac{3}{b}}=k^{\frac{1}{a}+\frac{1}{c}}\\\\\\\bold{\dfrac{3}{b}=\dfrac{1}{a}+\dfrac{1}{c}}\quad \checkmark[/tex]
