x^2-y^2=2011 x^2-y^2=2011 @Mathematics

Question

hero · Answer

(x+y)(x-y) = 2011

anonymous · Answer

Proceed :) please :) sorry

hero · Answer

This looks like a circle problem

anonymous · Answer

Its part of a problem from this txml competition

anonymous · Answer

what is the question?

hero · Answer

Oh, it's a hyperbola

hero · Answer

http://www.wolframalpha.com/input/?i=x%5E2-y%5E2%3D2011

anonymous · Answer

if you are supposed to find the integer solutions, then notice that 2011 is a prime number, so the only way that 
$$(x+y)(x-y)=2011$$ is if 
$$x+y=2011,x-y=1$$ and you can then solve for x and y

anonymous · Answer

it went something like the sum of integers equals the total distance traveled by plane. The difference between the squares of the two integers = 2011

anonymous · Answer

ok then you are looking for two integers that are one apart and add to 2011
 you get 1005 and 1006

anonymous · Answer

or i guess i should say you get 1006 for x and 1005 for y

hero · Answer

How on earth did you find that so fast?

anonymous · Answer

How did you find those two numbers?!!

hero · Answer

Oh nevermind. I didn't see that 2011 is a prime number

anonymous · Answer

because this is sort of the same as asking for a pythagorean triple where one side is 11
you put 
$$(x+y)(x-y)=11$$ meaning 
$$x+y=11,x-y=1$$ and pretty much solve in your head to get 
$$x=6,y=5$$

anonymous · Answer

hold on 
finding the numbers is not the hard part.  two numbers that are one apart and add to 2011

anonymous · Answer

the trick is recognizing that that is what you have to do

hero · Answer

And this the procedure when a number such as 2011 is a prime number, right?

hero · Answer

So if x^2-y^2 = 7, then x = 4 and y = 3?

anonymous · Answer

right

hero · Answer

:D

anonymous · Answer

then take 
$$2\times 4\times 3=24,4^2+3^2=25$$ and your right triangle is 
$$7,24,25$$

anonymous · Answer

Do you guys take the txml?

hero · Answer

The what?

anonymous · Answer

i took a taxi once

hero · Answer

lol

anonymous · Answer

hahha nevermind

hero · Answer

Is txml the new .xml format for excel?

anonymous · Answer

Nah its a math competition by the math league

hero · Answer

You're supposed to be at the math league man. What are you doing here? You're not going to win

anonymous · Answer

hahaha no I'm in this after school club and we take these

anonymous · Answer

How did you guys get so good at math? I love it, but I can't get good at it. I suck at problem solving