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guvirmaxim1
@guvirmaxim1
July 2022
1
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[tex] \left \{ {{log_{\frac{1}{3}}x+log_{ \frac{1}{3}} y=2 } \atop {log_{\frac{1}{2} }x-log_{\frac{1}{2}} y=4 } } \right. [/tex]
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Checov7400
(1) Log1/3(ху)=2Log1/3(1/3) (2) Log1/2(х/у)=4Log1/2(1/2)
Log1/3(ху)=Log1/3(1/3^2) Log1/2(х/у)=Log1/2(1/2^4)
ху=1/3^2 х/у=1/2^4
x=1/16 *у
подставим (2) в (1) ⇒ 1/16 *у²=1/9 ⇒ у²=16/9 ⇒ у=+/-√16/9=+/-4/3
у1=4/3 у2=-4/3
из(2) найдем х1=1/16 *4/3=1/12 х2=1/16 * -4/3=-1/12
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Checov7400
Ответ: х1 =1/12 у1=4/3=1целая1/3
Checov7400
х2 и у2 не являются решением данной системы по одз х должно быть >0 и у>0
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Answers & Comments
Log1/3(ху)=Log1/3(1/3^2) Log1/2(х/у)=Log1/2(1/2^4)
ху=1/3^2 х/у=1/2^4
x=1/16 *у
подставим (2) в (1) ⇒ 1/16 *у²=1/9 ⇒ у²=16/9 ⇒ у=+/-√16/9=+/-4/3
у1=4/3 у2=-4/3
из(2) найдем х1=1/16 *4/3=1/12 х2=1/16 * -4/3=-1/12