Решить уравнение log (127+x³)-3log(x+1)=0
Log(127+x³)-3*log(x+1)=0 ОДЗ: x>-1. x∈(-1;∞) log(127+x³)=3*log(x+1) log(127+x³)=log(x+1)³ 127+x³=(x+1)³ 127+x³=x³+3x²+3x+1 3x²+3x-126=0 |:3 x²+x-42=0 D=169 x₁=-7, x₂=6 -7∉(-1;∞). => x=-7 посторонний корень ответ: x=6
![\left \{ {{127+ x^{3} \ \textgreater \ 0} \atop {x+1\ \textgreater \ 0}} \right. , \left \{ {{ x^{3}\ \textgreater \ -127 } \atop {x\ \textgreater \ -1}} \right. , \left \{ {{x\ \textgreater \ \sqrt[3]{-127} } \atop {x\ \textgreater \ -1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B127%2B+x%5E%7B3%7D+%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%2B1%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+%2C++++%5Cleft+%5C%7B+%7B%7B+x%5E%7B3%7D%5C+%5Ctextgreater+%5C+-127+%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C+-1%7D%7D+%5Cright.+%2C++++%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C++%5Csqrt%5B3%5D%7B-127%7D+%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C+-1%7D%7D+%5Cright.+ "\left \{ {{127+ x^{3} \ \textgreater \ 0} \atop {x+1\ \textgreater \ 0}} \right. , \left \{ {{ x^{3}\ \textgreater \ -127 } \atop {x\ \textgreater \ -1}} \right. , \left \{ {{x\ \textgreater \ \sqrt[3]{-127} } \atop {x\ \textgreater \ -1}} \right.")