Ответ(ы) на вопрос:
Гость
[latex]lg(2-3x)+lg(2+3x)=lg(4-x)+lgx[/latex]
ОДЗ:
[latex] \left \{ {{2-3x\ \textgreater \ 0} \atop {2+3x\ \textgreater \ 0}}}} \right.[/latex]
[latex] \left \{ {{4-x\ \textgreater \ 0} \atop {x\ \textgreater \ 0}} \right. [/latex]
[latex] \left \{ {{x\ \textless \ \frac{2}{3} } \atop {x\ \textgreater \ - \frac{2}{3} }}}} \right. [/latex]
[latex] \left \{ {{x\ \textless \ 4} \atop {x\ \textgreater \ 0}} \right. [/latex]
[latex]x[/latex] [latex](0; \frac{2}{3} )[/latex]
[latex]lg[(2-3x)(2+3x)]=lg[(4-x)x][/latex]
[latex]lg(4-9x^2)=lg(4x-x^2)[/latex]
[latex]4-9x^2=4x-x^2[/latex]
[latex]8x^2+4x-4=0[/latex]
[latex]2x^2+x-1=0[/latex]
[latex]D=1^2-4*2*(-1)=9[/latex]
[latex]x_1= \frac{-1+3}{4}=0.5 [/latex]
[latex]x_2= \frac{-1-3}{4}=-1[/latex] ∅
Ответ: 0.5
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