Odpowiedzi

2010-02-01T00:07:59+01:00
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)
4 5 4