Odpowiedzi

2010-03-04T17:48:03+01:00
X⁴ + x²y² + y⁴ = 8 (z danych zadania)
(x² + y²)² - x²y² = 8
(x² + y² - xy)(x² + y² + xy) = 8
(x² + y² - xy)4 = 8
x² + y² - xy = 2

x² + xy + y² = 4 (z danych zadania)
x² + y² - xy = 2

odejmujemy stronami:
2xy = 2
xy = 1

x² + xy + y² = 4 (z danych zadania)
(x + y)² - xy = 4
(x + y)² = 4 + xy = 5

x² + y² - xy = 2
xy = 1
(x + y)² = 5

x⁶ + x³y³ + y⁶ = (x³ + y³)² - (xy)³ = ((x + y)(x² - xy + y²))² - (xy)³ = (x + y)²(x² - xy + y²)² - (xy)³ = 5*2² - 1³ = 5*4 - 1 = 19

jak masz pytania to pisz na pw