a³ + b³ = (a + b)(a² - ab + b²)
(a +- b)² = a² +- 2ab + b²
x^2y+xy^2=6
x^3+y^3=9
xy(x + y) = 6
(x + y)(x² - xy + y²) = (x + y)((x + y)² - 3xy) = 9
xy = b
x + y = a
ab = 6
a(a² - 3b) = 9
b = 6/a
a(a² - 3*6/a) = 9
a³ - 18 = 9
a³ = 27
a = 3
b = 2
xy = 2
x + y = 3
x = 3 - y
y(3 - y) = 2
y² - 3y + 2 = 0
D = 9 - 8 = 1
y12 = (3 +- 1)/2 = 1 2
y=1 x = 2/y = 2
y = 2 x = 2/y = 1
ответ (1,2)(2,1)
a³ + b³ = (a + b)(a² - ab + b²)
(a +- b)² = a² +- 2ab + b²
x^2y+xy^2=6
x^3+y^3=9
xy(x + y) = 6
(x + y)(x² - xy + y²) = (x + y)((x + y)² - 3xy) = 9
xy = b
x + y = a
ab = 6
a(a² - 3b) = 9
b = 6/a
a(a² - 3*6/a) = 9
a³ - 18 = 9
a³ = 27
a = 3
b = 2
xy = 2
x + y = 3
x = 3 - y
y(3 - y) = 2
y² - 3y + 2 = 0
D = 9 - 8 = 1
y12 = (3 +- 1)/2 = 1 2
y=1 x = 2/y = 2
y = 2 x = 2/y = 1
ответ (1,2)(2,1)