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Jonask

  • 3 years ago

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

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  1. Jonask
    • 3 years ago
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    \[\huge \color{brown}{ 2x^2+689x+c}\]

  2. Jonask
    • 3 years ago
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    @TuringTest @phi @hartnn @sauravshakya @shubhamsrg

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

  4. Jonask
    • 3 years ago
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    i dont kow wat to do here

  5. TuringTest
    • 3 years ago
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    @JamesJ D:

  6. Jonask
    • 3 years ago
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    first 689 can never be written as even number

  7. TuringTest
    • 3 years ago
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    I am pretty bad at things like this for some reason, sorry.

  8. Jonask
    • 3 years ago
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    thanks Turing

  9. Jonask
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=689

  10. Jonask
    • 3 years ago
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    wolfram gives interger solutions as \[c=689n-2n^2, x=-n\]

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

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

  13. shubhamsrg
    • 3 years ago
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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.

  14. Jonask
    • 3 years ago
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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

  15. Jonask
    • 3 years ago
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    is this the only c

  16. shubhamsrg
    • 3 years ago
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    What do you mean "the only c" ?

  17. Jonask
    • 3 years ago
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    the question says For how many positive integer values of c so are there 344 interger c's

  18. shubhamsrg
    • 3 years ago
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    yes.

  19. Jonask
    • 3 years ago
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    okay thanks

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