ParthKohli
  • ParthKohli
If \(x^a = y^b = z^c\) and \(y^2 = zx\), then the value of \(\dfrac{1}{a} + \dfrac{1}{c}\) is?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ParthKohli
  • ParthKohli
\[\dfrac{1}{a} + \dfrac{1}{c} = \dfrac{a + c}{ac}\]Any substitution?
shubhamsrg
  • shubhamsrg
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)
ParthKohli
  • ParthKohli
The choices are: 1. \(\dfrac{2}{b}\) and, 2. \(2a\)

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ParthKohli
  • ParthKohli
I have eliminated two more because they definitely are not the answers.
ParthKohli
  • ParthKohli
Ohhh!!
shubhamsrg
  • shubhamsrg
(2a-b)(2c-b) = b^2 4ac - 2ab - 2bc =0
ParthKohli
  • ParthKohli
Yeah, it's \(2/b\) by hit-and-trial
shubhamsrg
  • shubhamsrg
yep, just divide both sides by 2abc
ParthKohli
  • ParthKohli
HOW DID THAT NOT COME TO MY MIND?!
shubhamsrg
  • shubhamsrg
you must be busy with some of your research :)
ParthKohli
  • ParthKohli
-_-
shubhamsrg
  • shubhamsrg
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ParthKohli
  • ParthKohli
|dw:1361955168936:dw|
goformit100
  • goformit100
|dw:1361971686406:dw|

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