Question

Please solve this question. ​

Answer 1

Answer: see proof below

Explanation:

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

Then
`x^a=k\qquad \rightarrow \qquad x=k^{(1)/(a)}`

and
`y^b=k\qquad \rightarrow \qquad y=k^{(1)/(b)}`

and
`z^c=k\qquad \rightarrow \qquad z=k^{(1)/(c)}`

y³ = x · z

`(k^{(1)/(b)})^3=k^{(1)/(a)}\cdot k^{(1)/(c)}\\\\k^(3)/(b)}=k^{(1)/(a)+(1)/(c)}\\\\\\\bold{(3)/(b)=(1)/(a)+(1)/(c)}\quad \checkmark`