यदि `a^(x)= b, b^(y) = c` तथा `c^(z) = a` है , तब `1/((xy+yz+zx))(1/x+1/y+1/z)` का मान क्या है ?

Options

A. 0
B. abc
C. 1
D. `-1`

Answer

C

Explanation

दिया है , `1/((xy+yz+zx))(1/x+1/y+1/z)`
` = 1/((xy+yz+zx))xx((xy+yz+zx))/(xyz) = 1/(xyz)` ....(i)
`[:' x = (log b)/(log a) , y = (log c)/(log b) , z = (log a)/(log c)]`
` = (log a)/(log b) xx(log b)/(log x) xx(log c)/(log a ) = 1`