Question

If `(xy)^a=z,(yz)^a=x, and (xz)^a=y`, then what is the value of a? (None of x,y and z is either 0 or 1.)
A. 1
B. `(1)/(2)`
C. `(3)/(2)`
D. 0

Answer 1

Correct Answer - B
if `(xy)^a=z`
`*yz)^a=x`
`(xz)^a=y`
On multiplying Eqs. (1) , (2) , (3), we get
`(xyz)^2a=xyz`
`rArr (xyz)^2a=(xyz)^1`
`rArr (xyz)^2a=(xyz)^1`
`rArr 2a=1rArr a=(1)/(2)`
Hence, the correct option is (b).