Xy( x + y ) = 6
xy + ( x + y ) = 5
••••••••
xy = 6 : ( x + y )
( 6 : ( x + y ) ) + ( x + y ) = 5
x + y = a
( 6 : a ) + a = 5
6 + a^2 = 5a
a^2 - 5a + 6 = 0
D = 25 - 24 = 1 = 1^2
a1 = ( 5 + 1 ) : 2 = 3
a2 = ( 5 - 1 ) : 2 = 2
••••••••
x + y = 3
X = 3 - y
Xy + ( x + y ) = 5
y( 3 - y ) + 3 = 5
3y - y^2 - 2 = 0
y^2 - 3y + 2 = 0
D = 9 - 8 = 1 = 1^2
y1 = ( 3 + 1 ) : 2 = 2
y2 = ( 3 - 1 ) : 2 = 1
X = 3 - y
X1 = 3 - 2 = 1
X2 = 3 - 1 = 2
••••••••••••
X + y = 2
X = 2 - y
Xy + ( x + y ) = 5
y( 2 - y ) + 2 = 5
2y - y^2 - 3 = 0
y^2 - 2y + 3 = 0
D = 4 - 12 = - 8
Нет решений
Ответ ( 1 ; 2 ) ; ( 2 ; 1 )