If `a^x=b^y=c^z` and `abc=1` then find the value of `xy+yz+zx`

Options

A. 1
B. 3
C. 0
D. 5

Answer

C

Explanation

Here , ` a^(x) = b^(y) = c^(z)`
Let ` a^(x) = b^(y) = c^(z) = k`
` :. a = k^((1)/(x)) , b = k^((1)/( y)) and c = k^((1)/( z))`
`rArr abc = k ^(((1)/(x)+(1)/(y)+(1)/(z)))`
`:. abc = 1 " "` [ Given ]
` :. (1)/( x) + (1)/( y) + (1)/( z) = 0 `
` rArr xy + yz + zx = 0 `