Solve the following equations for all m & n in the set of all positive integers,
$\displaystyle m^2 + n^2 - m = 34$
$\displaystyle 2mn - n = 22$
Need some clues.......
Dear mathlover14,
$\displaystyle m^2 + n^2 - m = 34$----------(1)
$\displaystyle 2mn - n = 22$---------(2)
(1)+(2);
$\displaystyle (m+n)^2-(m+n)-56=0$-------(This is a quadratic equation. So find the two answers for m+n)
(1)-(2);
$\displaystyle (m-n)^2-(m-n)-12=0$--------(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.