aman07 Group Title Let * be a binary operation on Real numbers defined by a*b=ab/4 Given a*b=9 Find a and b one year ago one year ago

• This Question is Open
1. aman07 Group Title

help ! @TuringTest , @Mani_Jha , @dumbcow ,

2. mathslover Group Title

ok so we are given with the following information : a * b = ab/4 a*b = 9 this means $$\large{\frac{ab}{4} = 9}$$ , right ?

3. Hoa Group Title

yes

4. aman07 Group Title

yes

5. Hoa Group Title

---> ab =36

6. mathslover Group Title

Now , can you find what will be the value of "ab" ?

7. aman07 Group Title

ab=36 ?

8. Hoa Group Title

100010 =36

9. aman07 Group Title

but how i find value of a and b ?

10. mathslover Group Title

Yes right @aman07

11. mathslover Group Title

OK let me think for what to do after this, wait!

12. aman07 Group Title

ok

13. mathslover Group Title

What we have yet as a first way to get rid of this is "hit and trial" but really I don't think that hit and trial will be a satisfactory method ....

14. aman07 Group Title

well i knw to do that ..but there is some method using identity element and stuff

15. mathslover Group Title

http://www.math.csusb.edu/notes/binop/node2.html I saw something here

16. aman07 Group Title

:( i have that already in text.. i am stuck in this particular qn :(

17. Hoa Group Title

i got it now. you have ab =36 that means a=3 and b =6. in binary system, 3= 10 (one zero) and 6 = 1001. make multiplication between them , you got exactly 36 in both code (binary and 10 system)

18. aman07 Group Title

wth ??

19. goformit100 Group Title

ok

20. mathslover Group Title

I tried to search some relative problems on binary operations on internet and I found this question : if : $$\large{a\alpha b = |a-b| }$$ then what will be $$\large{6\alpha 8 }$$ . Of course that will be 2 but the question given is not exactly what we have in m

21. mathslover Group Title

In my question (contd. from the previous post.) Ok, I have never learnt it but I thought it is a type of mental ability question... Is it also related to binary numbers ?

22. Hoa Group Title

|dw:1361628824557:dw|

23. aman07 Group Title

nope ..i think no one understands the type of qn i am referring to ..leave it ..i am leaving thanks for trying to help

24. ParthKohli Group Title

@hoa "binary" doesn't mean "binary numbers"; it is just an operation you are doing with two numbers. Remember that "binary" stands for the numeral two.

25. mathslover Group Title

Don't get depressed from the help here given by me @aman07 ... we have at present many users seeing this question and I am sure that some people are still here who are aware of these type of problems. Just have patience aman... wait for them to respond

26. aman07 Group Title

ok

27. ParthKohli Group Title

We don't have sufficient information in this question.

28. ParthKohli Group Title

29. aman07 Group Title

no i do not have

30. ParthKohli Group Title

there are infinite ordered pairs of $$(a,b)$$.

31. mathslover Group Title

Yes right @ParthKohli . There is no sufficient information to solve for a and b.. though i can say : a = 36/b and b = 36/a :)

32. mathslover Group Title

but that values is where I am stuck ...

33. Hoa Group Title

lol, interesting question and interesting asker

34. ParthKohli Group Title

There are infinite values for $$(a,b)$$. We could have considered a particular pair if we had a much more restricted set/interval or the value of either of them.

35. ParthKohli Group Title

If you want to find $$ab$$, then it's 36 :-)

36. walters Group Title

let $x$element R be the identity with respect to * ,then x*a=a*x=a for all a element R now|dw:1361630564587:dw| |dw:1361630761828:dw|

37. mathteacher1729 Group Title

ab/4 = 9 means... Step 1: multiply a times b Step 2: divide by 4 the result is 9. That means 9*4 = a*b = 36 So a and b could be 9 and 4 or 18 and 2 or 3 and 12 or any two digits that multiply to 36. We'd need more information to narrow down the possibilities of what a and b could be. Are they both positive? Are they both positive integers? Are they both positive integers within a certain range? etc.

38. aman07 Group Title

well i am speAKing about the working given above by @walters using identity element but still i am having confusion

39. walters Group Title

where

40. walters Group Title

b*a does not neccesary means b multiply by a ,that's why i let x to identity knowing that i will have xa/4 and assign it to a but since a*b =9 this will also means that if a take x*a i will get the same value as a*b because of the binary operator

41. aman07 Group Title

can u explain it step by step pleas e?

42. aman07 Group Title

why doesnt b*a imply ba ?

43. aman07 Group Title

@walters ?

44. aman07 Group Title

i dont get the step ab=36 then how u write xa=36 ?

45. walters Group Title

because * (it is the star operator not multiplications) they are not equal

46. walters Group Title

|dw:1361638259187:dw|

47. aman07 Group Title

|dw:1361638483005:dw|

48. aman07 Group Title

b can be any number

49. walters Group Title

do u know the defination of the binary operator

50. aman07 Group Title

yes

51. walters Group Title

are doing Groups (abstract algebra)

52. aman07 Group Title

.

53. walters Group Title

ur questions means a*b if u take any 2 real numbers and map them the result will be in the form of multiplication of ur 2 real numbers divide by 4 and we know that tha mapping of those two numbers is equal to 9 tht's y i 've used 36 on my calculation because of the conditions i have