Explanation

m² + n² = 29 .......(1) m + n = 7 ............(2) From (2), m = 7 - n but m² + n² = 29, substituting; (7-n)² + n² = 29 49 - 14n + n² + n² = 29 => 2n² -14n + 20 = 0 Thus n² -7n + 10 = 0 Factorizing; (n-5)(n-2) = 0 n - 5 = 0, => n = 5 n - 2 = 0, => n = 2. When n = 5, m + n = 7, => m = 2, When n = 2, m + n = 7, => m = 5. Thus (m,n) = (5,2) and (2,5)

m² + n² = 29 .......(1) m + n = 7 ............(2) From (2), m = 7 - n but m² + n² = 29, substituting; (7-n)² + n² = 29 49 - 14n + n² + n² = 29 => 2n² -14n + 20 = 0 Thus n² -7n + 10 = 0 Factorizing; (n-5)(n-2) = 0 n - 5 = 0, => n = 5 n - 2 = 0, => n = 2. When n = 5, m + n = 7, => m = 2, When n = 2, m + n = 7, => m = 5. Thus (m,n) = (5,2) and (2,5)