Решите систему уравнений [tex] \left \{ {{x^2+y^2=2,5xy,} \atop {x-y=0,25xy. }} \right. [/tex]. Created by luhxor. algebra-ru

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luhxor @luhxor

August 2022 2 50 Report

Решите систему уравнений
[tex] \left \{ {{x^2+y^2=2,5xy,} \atop {x-y=0,25xy. }} \right. [/tex]

amin07am

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ProGroomer

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$\left\{\begin{array}{c}x^2+y^2=2.5xy\\x-y=0.25xy\end{array}\right\Rightarrow\left\{\begin{array}{c}(x-y)^2=2(0.25xy)\\x-y=0.25xy\end{array}\right\\(0.25xy)^2-2(0.25xy)=0\\\left\{\begin{array}{c}\left[\begin{array}{c}xy=0\\xy=8\end{array}\right\\x-y=0.25xy\end{array}\right\\\\1)\,x=0\Rightarrow y=0\,\,or\,\,y=0\Rightarrow x=0\\2)x={8\over y}\\{8\over y}-y=2\\{y^2+2y-8\over y}=0\\{(y+4)(y-2)\over y}=0\\y=-4\Rightarrow x=-2\,\,or\,\,y=2\Rightarrow x=4\\\\(-2;-4),\,(0;0),\,(4;2)$

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