Система уравнений {х^2-6ху+9у^2=16 х-у=6 - вопрос №60437852692166 от Olgaekolesnik 04.12.2021 10:51

Question

Алгебра: Система уравнений {х^2-6ху+9у^2=16 х-у=6

Olgaekolesnik · Answer

Х = y + 6
X^2 = y^2 + 12y + 36
y^2 + 12y + 36 - 6y( y + 6 ) + 9y^2 = 16
y^2 + 12y + 36 - 6y^2 - 36y + 9y^2 = 16
4y^2 - 24y + 20 = 0
4( y^2 - 6y + 5 ) = 0
D = 36 - 20 = 16 = 4^2
y1 = ( 6 + 4 ) : 2 = 5
y2 = ( 6 - 4 ) : 2 = 1
X = y + 6
X1 = 5 + 6 = 11
X2 = 1 + 6 = 7
ответ ( 11 ; 5 ) ; ( 7 ; 1 )