Question

Please solve this question. ​

Answer 1

Answer:  see proof below

Step-by-step explanation:

$x^a=y^b=z^c\ =k$

Then   $x^a=k\qquad \rightarrow \qquad x=k^{\frac{1}{a}}$

and    $y^b=k\qquad \rightarrow \qquad y=k^{\frac{1}{b}}$

and    $z^c=k\qquad \rightarrow \qquad z=k^{\frac{1}{c}}$

 y³ = x · z

$(k^{\frac{1}{b}})^3=k^{\frac{1}{a}}\cdot k^{\frac{1}{c}}\\\\k^\frac{3}{b}}=k^{\frac{1}{a}+\frac{1}{c}}\\\\\\\bold{\dfrac{3}{b}=\dfrac{1}{a}+\dfrac{1}{c}}\quad \checkmark$