if 2x 3y 6 z then 1 x y is, Surds and Indices, General Mathematics

Question:If` 2^x = 3^y = 6^-z,` then` (1/x + 1/y + 1/z)` is eequal to :

A 0 
B 1 
C `3/2` 
D `- 1/2`

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+ AnswerB

+ Explanation`2^x = 3^y = 6^-z`

`= k =>2 = k^(1/x), 3 = k^(1/y) & 6 = k^(- 1/z)`

Now `2 xx 3 = 6 => k^(1/x) xx k^(1/y)`

     `= k^(- 1/2) => k(1/x + 1/y)`

   `= k^(- 1/z)`

`:. 1/x + 1/y = - 1/z or 1/x + 1/y + 1/z = 1`

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