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Possible values of X and Y for the problem

  1. Sep 28, 2012 #1
    X and Y are whole nos
    X+Y= square of a no.
    X-Y=prime no.
    X*Y=twin no. (eg 77)
    X/Y=irrational no.

    how to solve such kind of problems apart from trial n error basis(ad hoc) ?
     
  2. jcsd
  3. Sep 28, 2012 #2
    If x and y are whole numbers, then x/y can't be irrational.
     
  4. Sep 28, 2012 #3
    sorry abt the fourth condition. what if first 3 conditions are considered ??

    X+Y= square of a no.
    X-Y=prime no.
    X*Y=twin no. (eg 77)

    what are the possible values of x and y. how to approach such a problem to narrow down our answers ??
     
  5. Sep 28, 2012 #4

    haruspex

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    Start with the last condition. What does that allow you to say about X and Y? (either one of them is 1 or ...?)
     
  6. Sep 28, 2012 #5
    The value of x or y can be 1 or 11. but all values of x with y being 1,will not satisfy the other two conditions. like
    99*1=99 but

    99-1=98 not a prime.

    so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

    is there any equation solving method and also can this question have a solution if at all ??
     
  7. Sep 28, 2012 #6
    99 = 3 * 33, so 1 and 11 aren't the only values x or y can take.

    There's 1 solution to your problem.

    Don't be surprised that you're getting "ad hoc" methods, you've thrown together a few random arbitrary conditions, especially the "twin number" bit.
     
  8. Sep 28, 2012 #7
    thank u abacus.

    i think the answer is 22 and 3.

    22*3=66

    22-3=19

    22+3=25
     
  9. Sep 28, 2012 #8

    haruspex

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    Ok, I misunderstood. I thought by "twin" number you meant a semiprime. You just mean two digits the same, right?
    Typically there are no equations for these sorts of problems. The technique is to start with the pieces of information that narrow down the possibilities fastest.
    Btw, for X*Y there are also possibilities like 3*22, etc.
     
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