Помогите срочно!! Реши систему уравнений: ⎧⎩⎨1x+y+1x−y=158x+y+10x−y=136 ⎧⎩⎨⎪⎪⎪⎪⎪...

2007roxana @2007roxana

July 2022 1 28 Report

Помогите срочно!!
Реши систему уравнений:
⎧⎩⎨1x+y+1x−y=158x+y+10x−y=136

⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪x=
y=
(Дробь в ответе должна быть сокращённой).

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Universalka

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$\left\{\begin{array}{ccc}\dfrac{1}{x+y}+\dfrac{1}{x-y}=15 \\\dfrac{8}{x+y}+\dfrac{10}{x-y}=136 \end{array}\right \\\\\\\dfrac{1}{x+y}=m \ ; \ \dfrac{1}{x-y}=n \\\\\\\left\{\begin{array}{ccc}m+n=15\\8m+10n=136\end{array}\right\\\\\\\left\{\begin{array}{ccc}m+n=15 \ |\cdot(-5)\\4m+5n=68\end{array}\right\\\\\\+\left\{\begin{array}{ccc}-5m-5n=-75\\4m+5n=68\end{array}\right\\-----------\\-m=-7\\\\m=7\\\\n=15-m=15-7=8\\\\1)\dfrac{1}{x+y}=7\\\\x+y=\dfrac{1}{7}\\\\2)\dfrac{1}{x-y}=8$

$x-y=\dfrac{1}{8} \\\\+\left\{\begin{array}{ccc}x+y=\dfrac{1}{7}\\x-y=\dfrac{1}{8}\end{array}\right \\--------\\2x=\dfrac{15}{56}\\\\x=\dfrac{15}{112}\\\\y=\dfrac{1}{7}-x=\dfrac{1}{7}-\dfrac{15}{112}=\dfrac{16-15}{112}=\dfrac{1}{112}\\\\\boxed{x=\dfrac{15}{112} \ ; \ y=\dfrac{1}{112}}$

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