Given that x and y are positive integers, solve the equation
x^2-4y^2=37

Question

Given that x and y are positive integers, solve the equation
x^2-4y^2=37

directrix · Answer

Mr. Wolf cranked out ± 19 for x and ± 9 for y. Look at the graph - it is a hyperbola. Follow the link: http://www.wolframalpha.com/input/?i=x%5E2+-+4y%5E2+%3D+37

anonymous · Answer

But how do I show the working?

directrix · Answer

I'll begin the solution for x and you can afterwards do so for y.

Before that, though, the question states that x and y are positive integers, so the answers are 19 for x and 9 for y. Those are answers and not solutions. The solution is comprised of the answer and how it was obtained.

nikvist · Answer

$$x^2-4y^2=(x-2y)(x+2y)=37=1\cdot 37$$$$x-2y=1\quad,\quad x+2y=37\quad\Rightarrow\quad x=19\quad,\quad y=9$$

anonymous · Answer

But how do I know that x-2y is equal to 1 while x+2y is equal to 37? :O

nikvist · Answer

You have two choices:
1.$$x-2y=1\quad,\quad x+2y=37\quad\Rightarrow\quad x=19\quad,\quad y=9$$2.$$x-2y=37\quad,\quad x+2y=1\quad\Rightarrow\quad x=19\quad,\quad y=-9\not\in\mathbb{N}$$

anonymous · Answer

Ok. Thank you so much!