Решите систему уравнений, пожалуйста. Created by noobmaster692. algebra-ru

Решите систему уравнений, пожалуйста...

noobmaster692 @noobmaster692

July 2022 1 6 Report

Решите систему уравнений, пожалуйста

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Ответ:

$\left\{\begin{array}{l}lgx+lgy=1+lg2\\2^{x-6}\cdot 2^{y}=64\end{array}\right\ \ \left\{\begin{array}{l}lg(xy)=lg10+lg2\\2^{x-6+y}=2^6\end{array}\right\ \ \left\{\begin{array}{l}lg(xy)=lg(10\cdot 2)\\x-6+y=6\end{array}\right$

$\left\{\begin{array}{l}xy=20\\x+y=12\end{array}\right\ \ \left\{\begin{array}{l}y=12-x\\x(12-x)=20\end{array}\right\ \ \left\{\begin{array}{l}y=12-x\\12x-x^2=20\end{array}\right\ \ \left\{\begin{array}{l}y=12-x\\x^2-12x+20=0\end{array}\right$

$\left\{\begin{array}{l}y_1=10\ ,\ y_2=2\\x_1=2\ ,\ x_2=10\\ODZ:x>0\ ,\ y>0\end{array}\right\ \ \ \ \ \ Otvet:\ \ (2;10)\ ,\ (10;2)\ .$

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