Question

Решите уравнение !!!!!!!!!

㏒₃x - ㏒₃(x² - 6)=0

Answer 1

ОДЗ: 1) x > 0               2) x² - 6 > 0
                                        (x - √6 )(x + √6 ) > 0
                                             +                -                +
                                        _______________________
                                                     -√6               √6
ОДЗ : x ∈ ( √6 ; + ∞)      

$log _{3}x-log _{3} ( x^{2} -6)=0\\log _{3} frac{x}{ x^{2} -6} =0\\ frac{x}{ x^{2} -6} =1\\ frac{x}{ x^{2} -6} -1=0\\ frac{x- x^{2} +6}{ x^{2} -6} =0$

- x² + x + 6 = 0                 x² - 6 ≠ 0
x² - x - 6 = 0
D = (-1)² - 4 * 1 * (- 6) = 1+24 = 25 = 5²
$x _{1} = frac{1+5}{2} =3\x _{2}= frac{1-5}{2}= - 2$
x = - 2 - не подходит
Ответ: 3

Answer 2

$log_3x-log_3(x^2-6)=0; ,\\ODZ:; left { {{x textgreater 0} atop {x^2-6 textgreater 0}} right. ; left { {{x textgreater 0} atop {(x-sqrt6)(x+sqrt6) textgreater 0}} right. ; ; to ; ; xin (sqrt6,+infty )\\log_3x=log_3(x^2-6); ; Rightarrow ; ; ; x=x^2-6\\x^2-x-6=0\\x_1=-2notin ODZ; ,; ; x_2=3; ; ; (teorema; Vieta)\\Otvet:; ; x=3; .$