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Please help me

  1. Oct 16, 2007 #1
    i m hashim i want to solve a qquestion
    1.if x is rational & y is irrational proof x+y is irrational???
    2. if x not equal to zero...y irrational proof x\y is irrational??
    3.if x,y is irrational ..dose it implise to x+y is irrational or x*y is irrational

    Last edited by a moderator: Oct 16, 2007
  2. jcsd
  3. Oct 16, 2007 #2
    1. is easy, what have you tried so far?
    2. Do you mean x/y? And is x supposed to be rational? If not then 2 is false.
  4. Oct 16, 2007 #3
    1. since x rational we can write it as p/q, where they cannot be simplifyed anymore.
    suppose now that x+y is rational,
    so it also can be written like r/s, where r,s are integers
    so x+y=r/s,

    p/q +y=r/s , y=r/s -p/q, so we come to a contradiction, since the right hand of the equation is also a rational, but it contradicts the fact that y is irrational, so our first assumtion that x+y is rational is wrong.
  5. Oct 16, 2007 #4
    3. for the it looks like trivial.
  6. Oct 16, 2007 #5
    what it mean????

    & where num 2 proof

  7. Oct 16, 2007 #6
    well, i am not going to show u the whole proof for the last one. But try to reason the same way i did on problem 1.
  8. Oct 16, 2007 #7
    mr sutupidmath ....
    czn u say my proof for 2
    since x non zerc, so x either rational or irrational
    i. if x rational & x non zero.......
    x =p\q wher p,q is intger...
    y is irrational.
    now suppose x\y is rastional
    x\y=r\s....r,s is integer.
    y=(s\r)*(p\q).....which is rational....contradict
    ii. x is irratinal, x non zero....y irrational
    suppose x\y = r\s
    x = r\s*y.........how to continue now?????

    please help me???
  9. Oct 17, 2007 #8


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    Science Advisor

    The way you have stated it, "2. if x not equal to zero...y irrational proof x\y is irrational", it's NOT true! For example, [itex]\pi/\pi= 1[/itex]. The ratio of two irrational numbers certainly can be rational. You probably meant: If x is a rational number, not equal to 0, and y is irrational, then x/y is irrational. For all of these, you don't need to go back to the definition of rational numbers as m/n. Use the fact that the rational numberse are closed under the operations of addition, subtraction, multiplication, and division (with divisor not 0).
  10. Oct 17, 2007 #9
  11. Oct 17, 2007 #10
  12. Oct 17, 2007 #11
    ok then, what could we say as a conclusion at this case. Because obviously we cannot conclude that at any case when x and y are irrational x/y is rational. FOr example, sqr3/sqr2 is irrational, or sqr6/sqr3, is obviously irrational.
  13. Oct 17, 2007 #12
    You can't say anything, sometimes it's rational, sometimes it isn't.
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