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



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

shubhamsrg
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x^2a = z^b . x^b = z^2c
x^(2ab) = z^b
and
z^(2cb) = x^b
or
(2ab) logx = b logz
and
b logx = (2cb)log z
=> (2ab)/b = b/(2cb)

ParthKohli
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The choices are:
1. \(\dfrac{2}{b}\) and, 2. \(2a\)

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

ParthKohli
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Ohhh!!

shubhamsrg
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(2ab)(2cb) = b^2
4ac  2ab  2bc =0

ParthKohli
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Yeah, it's \(2/b\) by hitandtrial

shubhamsrg
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yep, just divide both sides by 2abc

ParthKohli
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HOW DID THAT NOT COME TO MY MIND?!

shubhamsrg
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you must be busy with some of your research :)

ParthKohli
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_

shubhamsrg
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dw:1361955141551:dw

ParthKohli
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dw:1361955168936:dw

goformit100
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dw:1361971686406:dw