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Alb9
@Alb9
August 2022
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x^2+y^2=13; x+xy+y=-7 Это система. Как решать? Помогите, пожалуйста.
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infkoktnet
X+y = -7-xy
(x+y)^2 = (-7-xy)^2
x^2 + 2xy + y^2 = 49 + 14xy + (xy)^2
13 + 2xy = 49 + 14xy + (xy)^2
(xy)^2 + 12xy + 36 =0
Замена t = xy
t^2+12t+36 = 0
(t+6)^2 = 0
t =- 6
xy = -6
x+y = -7 - (-6) = -1
Система Виета
xy = -6
x+y = -1
Ответ: x1 = -3, y1 = 2
x2 = 2, y2 = -3
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Answers & Comments
(x+y)^2 = (-7-xy)^2
x^2 + 2xy + y^2 = 49 + 14xy + (xy)^2
13 + 2xy = 49 + 14xy + (xy)^2
(xy)^2 + 12xy + 36 =0
Замена t = xy
t^2+12t+36 = 0
(t+6)^2 = 0
t =- 6
xy = -6
x+y = -7 - (-6) = -1
Система Виета
xy = -6
x+y = -1
Ответ: x1 = -3, y1 = 2
x2 = 2, y2 = -3