2/7-lgx + 9/11+lgx = 13/12

[chokuuu]

Благодаря предварително.

2/7-lgx + 9/11+lgx = 13/12

[Гост]

[tex]\frac{2}{7-\lg{x}}+\frac{9}{11+\lg{x}}=\frac{13}{12}[/tex]
ДМ: [tex]\lg{x}\ne 7, \lg{x}\ne 9[/tex]
Полагаме [tex]y=\lg{x}[/tex]
[tex]\frac{2}{7+y}+\frac{9}{11+y}=\frac{13}{12}\Leftrightarrow \frac{22+2y+63+9y}{77+18y+y^2}=\frac{13}{12}\Leftrightarrow (11y+85)12=13(77+18y+y^2)\Leftrightarrow 132y+1020=1001+234y+13y^2 \Leftrightarrow 13y^2+102y-19=0[/tex]. [tex]D=8^.178[/tex], [tex]x_{1,2}=\frac{-102\pm 8\sqrt{178}}{26}=-51\pm 4\sqrt{178}[/tex].
[tex]\Rightarrow x_{1,2}=10^{-51\pm4\sqrt{178}}[/tex]

[ganka simeonova]

Благодаря предварително.

2/7-lgx + 9/11+lgx = 13/12