Znajdź wszystkie pary liczb całkowitych,których różnica kwadratów wynosi : 23 . -Układ równań .

x, y - liczby całkowite x² - y² = 23 (x-y)*(x+y) = 23 <=>( x-y =1 ∧ x +y = 23) ∨ ( x-y = 23 ∧ x+y = 1)∨ ∨(x-y = -1 ∧ x+y = -23) ∨ ( x-y = -23 ∧ x+y = -1 ) 1⁰ x-y = 1 ∧ x+y = 23 2x = 24 x = 12 y = x-1 = 12 - 1 = 11 2⁰ x-y = 23 ∧ x + y = 1 2x = 24 x = 12 y = x-23 = 12 - 23 = -11 3⁰ x-y = -1 ∧ x +y =- 23 2x = -24 x = -12 y = x +1 = -12 +1 = -11 4⁰ x -y = -23 ∧ x + y = -1 2x = -24 x = -12 y = x + 23 = -12 +23 = 11 Odp.(12;11),(12;-11), (-12;-11),(-12;11)