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Question

If 3x=4y=12z ,then prove that (x+y)z=xy.


Solution

3^x = 4^y = 12^z 
take 3^x = 12^z 

3 = 12^(z/x).......(1) 
take 4^y =12^z 

4 = 12^(z/y).......(2) 

multiply equation (1) and (2). 
you get 12 =12^(z/x + z/y) 
equating the powers on both sides : 
1 = z/x + z/y 
xy/(x+y)=z

(x+y)z=xy

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