1/x + 1/y + 1/z is equal to

If 2x = 3y = 6-z then 1/x + 1/y + 1/z is equal to
(a) 3/2
(b) 1
(c) 0
(d) -1/2

Anurag Mishra Professor Asked on 2nd April 2016 in Maths.
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1 Answer(s)

Answer:  (c) 0 

Solution:-
Let 2x = 3y = 6-z = k
2x = k
Therefore,  k^1/x = = 2

Similarly, k^1/y= 3 and k^-1/z = 6
=> k^-1/z = 2 x 3
= k^-1/z = k^1/x + k^1/y
= k^-1/z = k^(1/x + 1/y)
Comparing on both side,
-1/z = 1/x + 1/y
Therefore,
1/x + 1/y + 1/z = 0 .

Hence, the correct answer is option (c) 0.

Anurag Mishra Professor Answered on 3rd April 2016.
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