Решите систему уравнений: [tex] \left \{ {{x-y=3} \atop {x^{2+ y^{2} } =25-2xy}} \right. [/tex]. Created by yackupovaliyaЛия. algebra-ru

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Решите систему уравнений:

[tex] \left \{ {{x-y=3} \atop {x^{2+ y^{2} } =25-2xy}} \right. [/tex]

ВладимирБ

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Решение смотри в приложении

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yellok $\left \{ {{x-y=3} \atop { x^{2} +y^{2}=25-2xy}} \right. \left \{ {{x-y=3} \atop { x^{2} +2xy+y^{2}=25}} \right. \left \{ {{x-y=3} \atop { (x+y)^{2}=25}} \right. \left \{ {{x-y=3} \atop { x+y=5}} \right.$
или
$\left \{ {{x-y=3} \atop {x+y=-5}} \right.$
1) $\left \{ {{x-y=3} \atop { x+y=5}} \right.$ (+) ⇒ x-y+x+y=3+5
2x=8
x=8:2
x=4
y=x-3=4-3=1
ответ: (4; 1)
2) $\left \{ {{x-y=3} \atop {x+y=-5}} \right.$ (+) ⇒ x-y+x+y=3-5
2x=-2
x=-1
y=x-3=-1-3=-4
ответ: (-1; -4)

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