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ParthKohli Group Title

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

  • one year ago
  • one year ago

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

    • one year ago
  2. shubhamsrg Group Title
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    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)

    • one year ago
  3. ParthKohli Group Title
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    The choices are: 1. \(\dfrac{2}{b}\) and, 2. \(2a\)

    • one year ago
  4. ParthKohli Group Title
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    I have eliminated two more because they definitely are not the answers.

    • one year ago
  5. ParthKohli Group Title
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    Ohhh!!

    • one year ago
  6. shubhamsrg Group Title
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    (2a-b)(2c-b) = b^2 4ac - 2ab - 2bc =0

    • one year ago
  7. ParthKohli Group Title
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    Yeah, it's \(2/b\) by hit-and-trial

    • one year ago
  8. shubhamsrg Group Title
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    yep, just divide both sides by 2abc

    • one year ago
  9. ParthKohli Group Title
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    HOW DID THAT NOT COME TO MY MIND?!

    • one year ago
  10. shubhamsrg Group Title
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    you must be busy with some of your research :)

    • one year ago
  11. ParthKohli Group Title
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    -_-

    • one year ago
  12. shubhamsrg Group Title
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    |dw:1361955141551:dw|

    • one year ago
  13. ParthKohli Group Title
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    |dw:1361955168936:dw|

    • one year ago
  14. goformit100 Group Title
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    |dw:1361971686406:dw|

    • one year ago
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