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Ishaan94 Group Title

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

  • 2 years ago
  • 2 years ago

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  1. estudier Group Title
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    K, so what's y?

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

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

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

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

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

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

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

    • 2 years ago
  9. Ishaan94 Group Title
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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?

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

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

    • 2 years ago
  12. estudier Group Title
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    11 +

    • 2 years ago
  13. Ishaan94 Group Title
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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.

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

    • 2 years ago
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