Question

lg(х+√3)+lg(х-√3)=0 как решить ?

Answer 1

lg(x+√3)+lg(x-√3)=0
ОДЗ:
$left { {{x+ sqrt{3} textgreater 0 } atop {x- sqrt{3} textgreater 0}} right. , left { {{x textgreater - sqrt{3} } atop {x textgreater sqrt{3} }} right. = textgreater$
x>√3
lg((x+√3)*(x-√3))=0
lg(x²-(√3)²)=0
lg(x²-3)=0
x²-3=10⁰
x²-3=1
x²=4
x₁=-2, x₂=3
-2<√3, => x=-2 посторонний корень
ответ: х=2

Answer 2

$lg(x+sqrt3)+lg(x-sqrt3)=0\O.D.3.:;\begin{cases}x+sqrt3 textgreater 0\x-sqrt3 textgreater 0end{cases}Rightarrowbegin{cases}x textgreater -sqrt3\x textgreater sqrt3end{cases}Rightarrow x textgreater sqrt3\log_ab+log_ac=log_a(bcdot c)\lg(x+sqrt3)(x-sqrt3)=0\lg(x^2-3)=0\x^2-3=10^0\x^2-3=1\x^2=4\x_1=2\x_2=-2;-;He;nogx.;no;O.D.3.\OTBET:;x=2$