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Ishaan94

  • 2 years ago

Find all the integral solutions of the equation \(8y + 11x + 17 =xy\).

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  1. estudier
    • 2 years ago
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    K, so what's y?

  2. estudier
    • 2 years ago
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    (11x + 17) / (x-8) = y , right? Dunno if this is any good or not...

  3. estudier
    • 2 years ago
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    Need to break that up somehow....

  4. estudier
    • 2 years ago
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    11 + 105/(x-8)

  5. estudier
    • 2 years ago
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    So 105/(x-8) must be integer......

  6. estudier
    • 2 years ago
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    Exhaustion/look for a pattern takes care of that, I think...

  7. Ishaan94
    • 2 years ago
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    105 = 5*7*3*1. So, 8 integral solutions? Am I doing it right?

  8. estudier
    • 2 years ago
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    It's x we want....

  9. Ishaan94
    • 2 years ago
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    5*7. 2 more. 5*3. 2 more. 7*3. 2 more. and 105 itself. 2 more integral solutions. I mean x-8 could be \(\pm5,7,3,1,5*7,5*3,105,7*3\), Right?

  10. estudier
    • 2 years ago
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    Ther u go....

  11. estudier
    • 2 years ago
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    Then the y's

  12. estudier
    • 2 years ago
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    11 +

  13. Ishaan94
    • 2 years ago
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    Thanks. :-) Don't worry, I don't need the y's. I only need to show the total number of solutions are 16.

  14. Ishaan94
    • 2 years ago
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    In the actual question, that is.

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