Question

Lg (9-x)+2 lg 1/x+3=0

Answer 1

$lg (9 - x) + 2lg dfrac{1}{x}+3 = 0$

ОДЗ: $left{begin{array}{ccc}9 - x> 0\dfrac{1}{x} > 0 \end{array}right left{begin{array}{ccc}x < 9\x > 0 \end{array}right Rightarrow x in (0; 9)$

$lg (9 - x) + lg dfrac{1}{x^{2}} + lg 1000 = 0$

$lg dfrac{1000(9-x)}{x^{2}} = lg 1$

$dfrac{9000 - 1000x}{x^{2}} = 1$

$9000 - 1000x = x^{2}$

$x^{2} + 1000x - 9000 = 0$

$D = 1000^{2} - 4 cdot 1 cdot (-9000)= 1000000 + 36000 = 1036000$

$x_{1} = dfrac{-1000 + 20sqrt{2590}}{2} = -500 + 10sqrt{2590}$

$x_{2} = dfrac{-1000 - 20sqrt{2590}}{2} = -500 - 10sqrt{2590} notin (0; 9)$

Ответ: $x = -500 + 10sqrt{2590}$