Question

If \(x^a = y^b = z^c\) and \(y^2 = zx\), then the value of \(\dfrac{1}{a} + \dfrac{1}{c}\) is?

Answer 1

\[\dfrac{1}{a} + \dfrac{1}{c} = \dfrac{a + c}{ac}\]Any substitution?

Answer 2

x^2a = z^b . x^b = z^2c

x^(2a-b) = z^b
and
z^(2c-b) = x^b

or
(2a-b) logx = b logz
and
b logx = (2c-b)log z

=> (2a-b)/b = b/(2c-b)

Answer 3

The choices are:

1. \(\dfrac{2}{b}\) and, 2. \(2a\)

Answer 4

I have eliminated two more because they definitely are not the answers.

Answer 5

Ohhh!!

Answer 6

(2a-b)(2c-b) = b^2

4ac - 2ab - 2bc =0

Answer 7

Yeah, it's \(2/b\) by hit-and-trial

Answer 8

yep, just divide both sides by 2abc

Answer 9

HOW DID THAT NOT COME TO MY MIND?!

Answer 10

you must be busy with some of your research :)

Answer 11

-_-