bpt lôgảit

Question

Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,\frac{{\sqrt {x - 5} }}{{{{\log }_{\sqrt 2 }}\left( {x - 4} \right) - 1}} \ge
0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,\frac{{{{\log }_{\sqrt 2 }}{{\left( {x - 3} \right)}^2}}}{{{x^2} - 4x - 5}} \ge
0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$

score 4 · Answer 1

Bình chọn tăng 4 Bình chọn giảm

1) Điều kiện: $\left\{ \begin{array}{l} x\ge5\\\log_\sqrt2(x-4)\ne1 \end{array} \right.\Leftrightarrow \left\{ \begin{array}{l} x\ge5\\x\ne4+\sqrt2 \end{array} \right.$
Ta có: $\frac{\sqrt{x-5}}{\log_\sqrt2(x-4)-1}\ge0$
$\Leftrightarrow \log_\sqrt2(x-4)-1>0$
$\Leftrightarrow x-4>\sqrt2$
$\Leftrightarrow x>4+\sqrt2$
Kết hợp với ĐK: $x\in(4+\sqrt2,+\infty)$