Latest Lists

Methods to answer this math problem: list all ordered pairs...?

----------------------------------- (x^2+y) - (x+y^2) = 38 List all ordered pairs of integers (x,y) that satisfy this. ----------------------------------- What are some good methods to solve this?

Public Comments

1. (x^2 + y) - (x + y^2) = 38 Rearrange : (x^2 - y^2) - (x - y) = 38 Factorise left-hand term : (x - y)(x + y) - (x - y) = 38 Take out the factor, (x - y) : (x - y)(x + y - 1) = 38 Now we've made 38 as a product of 2 factors. Draw up a list of factors of 38 : (1) -1 * - 38 = 38 (2) -2 * -19 = 38 (3) 1 * 38 = 38 (4) 2 * 19 = 38 That's all! (1a) Let x - y = -1 and x + y - 1 = -38 This gives x = -19 and y = -18. (1b) Let x - y = -38 and x + y - 1 = -1 This gives x = -19 and y = 19. (2a) Let x - y = -2 and x + y - 1 = -19 This gives x = -10 and y = -8. (2b) Let x - y = -19 and x + y - 1 = -2 This gives x = -10 and y = 9. (3a) Let x - y = 1 and x + y - 1 = 38 This gives x = 20 and y = 19. (3b) Let x - y = 38 and x + y - 1 = 1 This gives x = 20 and y = -18. (4a) Let x - y = 2 and x + y - 1 = 19 This gives x = 11 and y = 9. (4b) Let x - y = 19 and x + y - 1 = 2 This gives x = 11 and y = -8. All ordered pairs (x, y) are therefore : (-19, -18), (-19, 19), (-10, -8), (-10, 9), (20, 19), (20, -18), (11, 9) and (11, - 8).