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

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

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yes
---> ab =36
Now , can you find what will be the value of "ab" ?
ab=36 ?
100010 =36
but how i find value of a and b ?
Yes right @aman07
OK let me think for what to do after this, wait!
ok
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 ....
well i knw to do that ..but there is some method using identity element and stuff
http://www.math.csusb.edu/notes/binop/node2.html I saw something here
:( i have that already in text.. i am stuck in this particular qn :(
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)
wth ??
ok
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
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 ?
|dw:1361628824557:dw|
nope ..i think no one understands the type of qn i am referring to ..leave it ..i am leaving thanks for trying to help
@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.
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
ok
We don't have sufficient information in this question.
Do you have the answer?
no i do not have
there are infinite ordered pairs of \((a,b)\).
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 :)
but that values is where I am stuck ...
lol, interesting question and interesting asker
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.
If you want to find \(ab\), then it's 36 :-)
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|
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.
well i am speAKing about the working given above by @walters using identity element but still i am having confusion
where
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
can u explain it step by step pleas e?
why doesnt b*a imply ba ?
i dont get the step ab=36 then how u write xa=36 ?
because * (it is the star operator not multiplications) they are not equal
|dw:1361638259187:dw|
|dw:1361638483005:dw|
b can be any number
do u know the defination of the binary operator
yes
are doing Groups (abstract algebra)
.
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

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