Question

помогите с уровнением сроочно

Answer 1

$(lg)^{2}+ lgx^{2} +lgx^{3} = 6\\(lg)^{2}+2lgx+3lgx = 6\\(lg)^{2} +5lgx = 6$

ОДЗ :

x > 0

Пусть lgx = t :

$t^{2} +5t = 6\\t^{2} +5t-6 = 0\\D = 25+4*6 = 25+24 = 49 = 7^{2} \\t1 = \frac{-5+7}{2} =\frac{2}{2} = 1\\t2 = \frac{-5-7}{2} =\frac{-12}{2} =-6$

-------------------

$lgx = 1\\x = 10^{1} = 10$

-------------------

$lgx = -6\\x = 10^{-6} =\frac{1}{10^{6} } = 0.000001$

Ответ : 10, 0.000001