## aman07 2 years ago Let * be a binary operation on Real numbers defined by a*b=ab/4 Given a*b=9 Find a and b

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1. aman07

help ! @TuringTest , @Mani_Jha , @dumbcow ,

2. mathslover

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

yes

4. aman07

yes

5. Hoa

---> ab =36

6. mathslover

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

7. aman07

ab=36 ?

8. Hoa

100010 =36

9. aman07

but how i find value of a and b ?

10. mathslover

Yes right @aman07

11. mathslover

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

12. aman07

ok

13. mathslover

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

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

15. mathslover

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

16. aman07

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

17. Hoa

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

wth ??

19. goformit100

ok

20. mathslover

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

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

|dw:1361628824557:dw|

23. aman07

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

@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

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

ok

27. ParthKohli

We don't have sufficient information in this question.

28. ParthKohli

29. aman07

no i do not have

30. ParthKohli

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

31. mathslover

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

but that values is where I am stuck ...

33. Hoa

lol, interesting question and interesting asker

34. ParthKohli

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

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

36. walters

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

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

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

39. walters

where

40. walters

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

can u explain it step by step pleas e?

42. aman07

why doesnt b*a imply ba ?

43. aman07

@walters ?

44. aman07

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

45. walters

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

46. walters

|dw:1361638259187:dw|

47. aman07

|dw:1361638483005:dw|

48. aman07

b can be any number

49. walters

do u know the defination of the binary operator

50. aman07

yes

51. walters

are doing Groups (abstract algebra)

52. aman07

.

53. walters

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