Решите систему уравнений методом замены переменных

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 )