Question

Log по основанию х+1 (х^2-х+1)>1

Answer 1

$log_{x+1}(x^2-x+1)\ \textgreater \ 1\\ D(y): x+1\ \textgreater \ 0,\ x+1 \neq 1, \ x^2-x+1\ \textgreater \ 0\\ x\ \textgreater \ -1, \ x \neq 0\\ x\in(-1;0)U(0;+\infty)\\ log_{x+1}(x^2-x+1)\ \textgreater \ log_{x+1}(x+1)\\ 1) \ 0\ \textless \ x+1\ \textless \ 1, \ -1\ \textless \ x\ \textless \ 0\\ x^2-x+1\ \textless \ x+1\\ x^2-2x\ \textless \ 0\\ x(x-2)\ \textless \ 0\\ \left \{ {{x\in(0;2)} \atop {x\in(-1;0)}} \right. \\ x\in \varnothing\\ 2) \ x+1\ \textgreater \ 1, \ x\ \textgreater \ 0\\ x^2-x+1\ \textgreater \ x+1\\ x^2-2x\ \textgreater \ 0\\ x(x-2)\ \textgreater \ 0\\ \left \{ {{x\in(-\infty;0)U(2;+\infty)} \atop {x\ \textgreater \ 0}} \right. \\ x\in(2;+\infty)$