1. ## Equations

Solve the following equations for all m & n in the set of all positive integers,

$m^2 + n^2 - m = 34$

$2mn - n = 22$

Need some clues.......

2. ## Re: Equations

Originally Posted by mathlover14
Solve the following equations for all m & n in the set of all positive integers,

$m^2 + n^2 - m = 34$

$2mn - n = 22$

Need some clues.......
Dear mathlover14,

$m^2 + n^2 - m = 34$----------(1)

$2mn - n = 22$---------(2)

(1)+(2);

$(m+n)^2-(m+n)-56=0$-------(This is a quadratic equation. So find the two answers for m+n)

(1)-(2);

$(m-n)^2-(m-n)-12=0$--------(Find the two answers for m-n)

So ultimately you will have four equations (two values for m+n and two values for m-n). Using these four equations in different combinations you will be able to get 4 different answer sets. Hope you can continue.