Question

Введите систему уравнений

Answer 1

1) ( 1/Х ) + ( 1/y ) = ( x + y ) / xy
2) 1 : ( ( x + y )/xy ) = xy / ( x + y )
3) xy / ( x + y ) = 15/4
xy / ( x + y ) = 3,75
Xy = 3,75( x + y )
4) x = y - 4
y( y - 4 ) = 3,75( y - 4 + y )
y^2 - 4y = 3,75( 2y - 4 )
y^2 - 4y = 7,5y - 15
y^2 - 11,5y + 15 = 0
D = 132,25 - 60 = 72,25 = 8,5^2
y1 = ( 11,5 + 8,5 ) : 2 = 10
y2 = ( 11,5 - 8,5 ) : 2 = 1,5
X = y - 4
X1 = 10 - 4 = 6
X2 = 1,5 - 4 = - 2,5
Ответ ( 6 ; 10 ) ; ( - 2,5 ; 1,5 )