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ParthKohli
 2 years ago
Why is my answer wrong?
Consider the function on the integers given by \(f(x,y)=x^2y\). How many ordered pairs of integers satisfying \(−16\le x,y\le16\) is \(f(x,y)=f(y,x)\)?
ParthKohli
 2 years ago
Why is my answer wrong? Consider the function on the integers given by \(f(x,y)=x^2y\). How many ordered pairs of integers satisfying \(−16\le x,y\le16\) is \(f(x,y)=f(y,x)\)?

This Question is Closed

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2\[f(x,y)=f(y,x) \Rightarrow y^2x = x^2 y \]I observed that \(x\) and \(y\) cannot be negative here. So I am left with numbers ranging from \(0\) to \(16\). That gives me \(17\).

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Are there any other ordered pairs where \(x \ne y\)?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2\((4)^2 \times 4 = (4)^2 \times 4\)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Facepalm. They can be negative.

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2PING and the light turns on!

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2lol yeah. That fetches me \(17 + 16 = 33\)

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2that many ordered pairs (0,?) and (?,0)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Oh, I'm stupid. Thanks man!

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2so, it'd be 33+32+32 ordered pairs

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2how many ways can you have 1) x=0 2) y=0 3) x=y

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2(1,1),(2,2)...(16,16) is 16. (1,1)...(16,16) is 16. (0,?) is 33. (?,0) is 33. 32 + 33 + 33 = 98 We overcounted a (0,0), so 32 + 32 + 33 = 97. Right?

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.0Is this from brilliant.org?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2@oldrin.bataku Yeah, practicing stuff :)

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2this way you counted (0,0) twice

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Am I not allowed to ask questions for practice?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2@electrokid I subtracted it in the end.

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not sure if you're allowed to ask for help on brilliant.org questions, at least publicly... :p

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2@oldrin.bataku But I think I'm just practicing techniques.

perl
 2 years ago
Best ResponseYou've already chosen the best response.0brilliant! 97 is the correct answer

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.2o'course it'd be lol

perl
 2 years ago
Best ResponseYou've already chosen the best response.0i said, i enjoyed the problem

perl
 2 years ago
Best ResponseYou've already chosen the best response.0now i must go , there are babies to punish
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