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

- anonymous

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

- schrodinger

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- anonymous

help ! @TuringTest , @Mani_Jha , @dumbcow ,

- 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 ?

- anonymous

yes

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- anonymous

yes

- anonymous

---> ab =36

- mathslover

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

- anonymous

ab=36 ?

- anonymous

100010 =36

- anonymous

but how i find value of a and b ?

- mathslover

Yes right @aman07

- mathslover

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

- anonymous

ok

- 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 ....

- anonymous

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

- mathslover

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

- anonymous

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

- anonymous

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)

- anonymous

wth ??

- goformit100

ok

- 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

- 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 ?

- anonymous

|dw:1361628824557:dw|

- anonymous

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

- 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.

- 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

- anonymous

ok

- ParthKohli

We don't have sufficient information in this question.

- ParthKohli

Do you have the answer?

- anonymous

no i do not have

- ParthKohli

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

- 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 :)

- mathslover

but that values is where I am stuck ...

- anonymous

lol, interesting question and interesting asker

- 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.

- ParthKohli

If you want to find \(ab\), then it's 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|

- 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.

- anonymous

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

- walters

where

- 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

- anonymous

can u explain it step by step pleas e?

- anonymous

why doesnt b*a imply ba ?

- anonymous

@walters ?

- anonymous

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

- walters

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

- walters

|dw:1361638259187:dw|

- anonymous

|dw:1361638483005:dw|

- anonymous

b can be any number

- walters

do u know the defination of the binary operator

- anonymous

yes

- walters

are doing Groups (abstract algebra)

- anonymous

.

- 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

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