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Ответ дал:
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Сначала найдем значение ху:
![left { {{x^2+y^2=75-xy} atop {x^2+y^2=25+xy}} right. \
25+xy=75-xy\
2xy=75-25=50\
xy=25](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx%5E2%2By%5E2%3D75-xy%7D+atop+%7Bx%5E2%2By%5E2%3D25%2Bxy%7D%7D+right.+%5C%0A25%2Bxy%3D75-xy%5C%0A2xy%3D75-25%3D50%5C%0Axy%3D25 "left { {{x^2+y^2=75-xy} atop {x^2+y^2=25+xy}} right. \
25+xy=75-xy\
2xy=75-25=50\
xy=25")
![x^2+xy+y^2=75\
+\
x^2-xy+y^2=75\
=\
2x^2+2y^2=100\
left { {{x^2+y^2=50} atop {2xy=50}} right. \
x^2+y^2=2xy\
x^2-2xy+y^2=0\
(x-y)^=0\
left { {{x-y=0} atop {xy=25}} right. \
left { {{x=y} atop {x^2=25}} right. \
x=y= sqrt{25}=5 \
x=y= sqrt{25}=-5](https://tex.z-dn.net/?f=x%5E2%2Bxy%2By%5E2%3D75%5C%0A%2B%5C%0Ax%5E2-xy%2By%5E2%3D75%5C%0A%3D%5C%0A2x%5E2%2B2y%5E2%3D100%5C%0A+left+%7B+%7B%7Bx%5E2%2By%5E2%3D50%7D+atop+%7B2xy%3D50%7D%7D+right.+%5C%0Ax%5E2%2By%5E2%3D2xy%5C%0Ax%5E2-2xy%2By%5E2%3D0%5C%0A%28x-y%29%5E%3D0%5C%0A+left+%7B+%7B%7Bx-y%3D0%7D+atop+%7Bxy%3D25%7D%7D+right.+%5C%0A+left+%7B+%7B%7Bx%3Dy%7D+atop+%7Bx%5E2%3D25%7D%7D+right.+%5C%0Ax%3Dy%3D+sqrt%7B25%7D%3D5+%5C%0Ax%3Dy%3D+sqrt%7B25%7D%3D-5 "x^2+xy+y^2=75\
+\
x^2-xy+y^2=75\
=\
2x^2+2y^2=100\
left { {{x^2+y^2=50} atop {2xy=50}} right. \
x^2+y^2=2xy\
x^2-2xy+y^2=0\
(x-y)^=0\
left { {{x-y=0} atop {xy=25}} right. \
left { {{x=y} atop {x^2=25}} right. \
x=y= sqrt{25}=5 \
x=y= sqrt{25}=-5")
Ответ дал:
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Я тут немного перемудрил, но вцелом все правильно.
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