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If (xy)^((a - 1)) = z, (yz)^((b - 1)) =...

If `(xy)^((a - 1)) = z, (yz)^((b - 1)) = x and (xz)^((c-1)) = y, and xyz` is not ` -1, 0 or 1`, then which of the following is equal to `ab + bc + ca?`

A

`abc`

B

`(abc)/2`

C

`2abc`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
(i) Expand and simplify each equation.
(ii) Use `a^(3)-b^(3)=(a-b) (a^(2)+b^(2)+ab)` and simpliy the exponents.
(iii) Check the bases of all the exponets and proceed.
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