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ParthKohli

  • 2 years ago

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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  1. ParthKohli
    • 2 years ago
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    \[\dfrac{1}{a} + \dfrac{1}{c} = \dfrac{a + c}{ac}\]Any substitution?

  2. shubhamsrg
    • 2 years ago
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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)

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

  4. ParthKohli
    • 2 years ago
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    I have eliminated two more because they definitely are not the answers.

  5. ParthKohli
    • 2 years ago
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    Ohhh!!

  6. shubhamsrg
    • 2 years ago
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    (2a-b)(2c-b) = b^2 4ac - 2ab - 2bc =0

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

  8. shubhamsrg
    • 2 years ago
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    yep, just divide both sides by 2abc

  9. ParthKohli
    • 2 years ago
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    HOW DID THAT NOT COME TO MY MIND?!

  10. shubhamsrg
    • 2 years ago
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    you must be busy with some of your research :)

  11. ParthKohli
    • 2 years ago
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    -_-

  12. shubhamsrg
    • 2 years ago
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    |dw:1361955141551:dw|

  13. ParthKohli
    • 2 years ago
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    |dw:1361955168936:dw|

  14. goformit100
    • 2 years ago
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    |dw:1361971686406:dw|

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