Решите систему уравнений). Created by leonidoviclev. algebra-ru

Решите систему уравнений)...

leonidoviclev @leonidoviclev

July 2022 1 21 Report

Решите систему уравнений)

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NNNLLL54

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Ответ:

$\left\{\begin{array}{l}2^{\frac{x+y}{3}}+2^{\frac{x+y}{6}}=6\\2x^2+10y^2=9xy\end{array}\right\\\\\\a)\ \ 2^{\frac{x+y}{3}}+2^{\frac{x+y}{6}}=6\ \ ,\ \ \ t=2^{\frac{x+y}{6}}>0\ \ ,\ \ t^2+t-6=0\ \ ,\ \ t_1=-3$

$x_1=\dfrac{29-1}{7}=4\ \ ,\ \ x_2=\dfrac{29+1}{7}=\dfrac{30}{7}=4\dfrac{2}{7}\\\\y_1=6-x_1=6-4=2\ \ ,\ \ y_2=6-x_2=6-\dfrac{30}{7}=\dfrac{12}{7}\\\\Otvet:\ \Big(4\, ;\, 2\, \Big)\ \ ,\ \ \Big(\ \dfrac{30}{7}\ ;\ \dfrac{12}{7}\ \Big)\ .$

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