Binary Operations

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§uperman

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Aug 16, 2009
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3
Hey,
um, Im new here, and im just assuming that i go straight in ad ask for help.
I was revising for the Aussie Maths olympiad, and i came across a question in the 2004 intermediate olypiad paper.
not sure exactly where to put this but post, but ...

A new binary operation ? defined on all positive integers x and y, satisfies the following conditions.
x?x = x+2
x?y = y?x
x?(x+y)/x?y = x+y/y
given the above, find 11?8

please explain how to do this question, and give an answer...

thanks in advance
 


Without grouping symbols, I cannot determine the ratio in the lefthand side of the third equation. Please clarify this algebraic fraction.

Here are some possibilities (followed by their LaTex versions):

[x?(x+y)]/[x?y] = [x+y]/y

\(\displaystyle \frac{x?(x+y)}{x?y} = \frac{x+y}{y}\)

x?[(x+y)/(x?y)] = [x+y]/y

\(\displaystyle x?\frac{x+y}{x?y} = \frac{x+y}{y}\)

([x?(x+y)]/x)?y = [x+y]/y

\(\displaystyle \frac{x?(x+y)}{x}?y = \frac{x+y}{y}\)

x?[(x+y)/x]?y = [x+y]/y

\(\displaystyle x?\frac{x+y}{x}?y = \frac{x+y}{y}\)

 
Its definitely the first equation that you showed, the one in my original post,
X?(X+Y)/X?Y = x+y/y
I thought that the X?'s in the LHS canceled out, I also know that it has an integer solution, but what do you mean by grouping symbols?


p.s How do u add LaTex to a post?
 
YESSS!!!!!!
I just figured it out...
i was making a really small substitution and adding mistake

8 ? 11 = 8 ? ( 8+3 ) = (8 ? 3) 11/3...
3 ? 8 = 3 ? ( 3+5) = (3 ? 5) 8/5
3 ? 5 = 3 ? ( 2+3 ) = (3 ? 2) 5/2
3 ? 2 = 2 ? (1 + 2) = (2 ? 1) 3/1
2 ? 1 = 1? (1 + 1) = (1 ? 1)2/1
1 ? 1 = 3

then work up...

giving 8 ? 11 = 264
please say if i am right
 
Buddhists spend their whole lives trying to live without want, but want to reach Nirvana
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Wrong my grasshopper ... Buddhists only AIM to reach nirvana .....
 
§uperman said:
Its definitely the first equation that you showed, the one in my original post …
Click to expand...


I think you missed my point.

The third equation in your original post is not clear, as typed.

Let me know, if you're interested in understanding the difference. I can explain the ambiguities in greater detail.

 
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