Помогите с логарифмами. [tex] \left \{ {{ log _{3}x+log _{3}y=1-log _{3}2} \atop {log _{3}(x+y)=2}} \right. [/tex]. Created by Exxclusive. algebra-ru

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Помогите с логарифмами.
[tex] \left \{ {{ log _{3}x+log _{3}y=1-log _{3}2} \atop {log _{3}(x+y)=2}} \right.
[/tex]

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skvrttt $\displaystyle\mathtt{\left\{{{\log_3x+\log_3y+\log_32=1}\atop{\log_3(x+y)=2}}\right\left\{{{\left\{{{\log_3(2xy)=1}\atop{x+y=9}}\right}\atop{\left\{{{x\ \textgreater \ 0}\atop{y\ \textgreater \ 0}}\right}}\right\left\{{{\left\{{{2xy=3}\atop{x=9-y}}\right}\atop{\left\{{{x\ \textgreater \ 0}\atop{y\ \textgreater \ 0}}\right}}\right}$

$\displaystyle\mathtt{\left\{{{\left\{{{2(9-y)y=3}\atop{x=9-y}}\right}\atop{\left\{{{x\ \textgreater \ 0}\atop{y\ \textgreater \ 0}}\right}}\right\left\{{{\left\{{{2y^2-18y+3=0}\atop{x=9-y}}\right}\atop{\left\{{{x\ \textgreater \ 0}\atop{y\ \textgreater \ 0}}\right}}\right\left\{{{\left\{{{\left[\begin{array}{ccc}\mathtt{y_1=\frac{9-5\sqrt{3}}{2}}\\\mathtt{y_2=\frac{9+5\sqrt{3}}{2}}\end{array}\right}\atop{x=9-y}}\right}\atop{\left\{{{x\ \textgreater \ 0}\atop{y\ \textgreater \ 0}}\right}}\right}$

ответ: $\mathtt{(\frac{9+5\sqrt{3}}{2};~\frac{9-5\sqrt{3}}{2})}$ или $\mathtt{(\frac{9-5\sqrt{3}}{2};~\frac{9+5\sqrt{3}}{2})}$

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odin iz kornej uravneniya 4x 20xc0 bolshe drugogo na 4 najdite c

17 mln 17 000 000 v standartnom vide

texbolshe drugogo na 4 najdite c

x 2s resheniem

pri kakih znacheniya x imeet smysl vyrazhenie 4 x2x 5 v otvete ukazhite nai

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