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Jonask Group Title

For how many positive integer values of c does the equation below have an integer solution?

  • one year ago
  • one year ago

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  1. Jonask Group Title
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    \[\huge \color{brown}{ 2x^2+689x+c}\]

    • one year ago
  2. Jonask Group Title
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    @TuringTest @phi @hartnn @sauravshakya @shubhamsrg

    • one year ago
  3. Jonask Group Title
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    \[(2x+a)(x+b)=4x^2+2x(a+b)+ab\] \[2(a+b)=689,ab=c\]

    • one year ago
  4. Jonask Group Title
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    i dont kow wat to do here

    • one year ago
  5. TuringTest Group Title
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    @JamesJ D:

    • one year ago
  6. Jonask Group Title
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    first 689 can never be written as even number

    • one year ago
  7. TuringTest Group Title
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    I am pretty bad at things like this for some reason, sorry.

    • one year ago
  8. Jonask Group Title
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    thanks Turing

    • one year ago
  9. Jonask Group Title
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    http://www.wolframalpha.com/input/?i=689

    • one year ago
  10. Jonask Group Title
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    wolfram gives interger solutions as \[c=689n-2n^2, x=-n\]

    • one year ago
  11. TuringTest Group Title
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    I am assuming the equation is\[\large2x^2+689x+c=0\]right?

    • one year ago
  12. Jonask Group Title
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    http://www.wolframalpha.com/input/?i=2x%5E2%2B689x%2Bc%3D0

    • one year ago
  13. shubhamsrg Group Title
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    2x^2 + 689x + c = 0 c = -689x - 2x^2 x= n will always given a -ve c, hence x should be -n , for some integer n, => c = 689n - 2n^2 this has to be >0 => 689n -2n^2 >0 => n(689 - 2n) >0\ We already know n>0 hence we only have to deal with 689 > 2n or n < 344.5 Hence there can be 344 required value's of c. I have done this on brilliant.org if I am not wrong.

    • one year ago
  14. Jonask Group Title
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    yes its from them,i have many other problems from them,if you dont mind you can check the question i asked bfore this one...thanks makes sense

    • one year ago
  15. Jonask Group Title
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    is this the only c

    • one year ago
  16. shubhamsrg Group Title
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    What do you mean "the only c" ?

    • one year ago
  17. Jonask Group Title
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    the question says For how many positive integer values of c so are there 344 interger c's

    • one year ago
  18. shubhamsrg Group Title
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    yes.

    • one year ago
  19. Jonask Group Title
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    okay thanks

    • one year ago
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