Lg(х+√3)+lg(х-√3)=0 как решить ?
Что значит "eg"?
lg
Решите задачу:
Lg(x+√3)+lg(x-√3)=0 ОДЗ: 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
![\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 \](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%2B+%5Csqrt%7B3%7D%5C+%5Ctextgreater+%5C+0+%7D+%5Catop+%7Bx-+%5Csqrt%7B3%7D+%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+%2C+++%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+-+%5Csqrt%7B3%7D+%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C++%5Csqrt%7B3%7D+%7D%7D+%5Cright.+%3D%5C+%5Ctextgreater+%5C+ "\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 \")