Question

ПОМОГИТЕ ПЛИЗ lg(2x-1)+lg(x-9)=2

Answer 1

$lg(2x-1)(x-9)=2$
$lg(2x-1)(x-9)=lg100$
$(2x-1)(x-9)=100$
$2x^{2}-18x-x+9-100=0$
$2x^{2}-19x-91=0, D=1089=33^{2}$
$x_{1}= \frac{19-33}{4}=- \frac{14}{4}=- \frac{7}{2}=-3.5<0$ - посторонний корень
$x_{2}= \frac{19+33}{4}= \frac{52}{4}=13>9$

ОДЗ:
$\left \{ {{2x-1\ \textgreater \ 0} \atop {x-9\ \textgreater \ 0}} \right.$

$\left \{ {{x\ \textgreater \ 0.5} \atop {x\ \textgreater \ 9}} \right.$

x>9

Ответ: х=13