+0  
 
+1
81
2
avatar+836 

Hello! I came across a probem that I'm stuck on! It is If \(x+\frac{1}{y}=1\) and \(y+\frac{1}{z}=1\), what is the value of the product \(xyz\)?

 

Do you have to expand or square it! Thanks!

 Nov 3, 2018
 #1
avatar+94545 
+2

x +  1/y  =  1

x  =  1 - 1/y  =      [ y - 1] / y

 

And

 

y + 1/z  =  1

1/z  =  1 - y    which implies that

z  =  1 / [ 1 - y]

 

 

 

So    x  y  z   =     

 

 ( [ y - 1] / y  )  * y *  [ 1 / ( 1 - y) ]    = 

 

[  y - 1 ]  *  [  1  / (1 - y) ]  =

 

-1 ( 1 - y)  *  [ 1 / (1 - y) ]  =

 

-1  

 

cool cool cool

 Nov 3, 2018
edited by CPhill  Nov 3, 2018
 #2
avatar+836 
+1

Thank you, CPhill! I understand it better, now!

ant101  Nov 4, 2018

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