Question

If a^x=b^y=c^z=ABC, then 1/X +1/y+1/z is equal to what?

Answer 1

Answer:

abc = a^x  

as  

2 x 3 x 6 = 2^5  

hence (2x3x6)^(1/5) = 2  

hence we can conclude  

abc = a^x  

(abc)^1/x = a  

hence the same results for a, b and c  

hence we can conclude (abc)^(1/y + 1/z + 1/x) = abc  

and abc = (abc)^1  

Since they all have the same bases,  

1/y + 1/z + 1/x = 1