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Giải các bất phương trình:
$\begin{array}{l}
1)\,\,\,{\left( {\sqrt 2 + 1} \right)^{\frac{{6x - 6}}{{x + 1}}}} \le {\left( {\sqrt 2 - 1} \right)^{ - x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\left( {\sqrt 5 + 2} \right)^{x - 1}} \ge {\left( {\sqrt 5 - 2} \right)^{\frac{{x - 1}}{{x + 1}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\,
\end{array}$
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Đăng bài 02-05-12 05:01 PM
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Đăng bài 27-04-12 08:33 AM
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Giải bất phương trình :
${x^{{{\log }_a}x + 1}} > {a^2}x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải và biện luận theo tham số $a$ :
$\begin{array}{l}
1)\,\,{a^2} - {9^{x + 1}} - 8a{.3^x} > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{a^2} - {2.4^{x + 1}} - a{.2^{x + 1}} > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Tìm các giá trị $m$ để bất phương trình sau đây có nghiệm :
$\begin{array}{l}
1)\,\,\,{3^{2x + 1}} - \left( {m + 3} \right){3^x} - 2\left( {m + 3} \right) < 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{4^x} - \left( {2m + 1} \right){2^x} + {m^2} + m \ge 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Tìm $m$ để mỗi bất phương trình sau đây có nghiệm:
$\begin{array}{l}
1)\,\,\,{4^x} - {5.2^x} + m \le 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3)\,\,\,{9^x} + m{.3^x} - 1 < 0\\
2)\,\,{4^x} + {5.2^x} + m > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4)\,\,{9^x} + m{.3^x} + 1 \le 0
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,\,{\left( {{2^x} + {{3.2}^{ - x}}} \right)^{2{{\log }_2}x - {{\log }_2}\left( {x + 6} \right)}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,\,\,{\left( {{{4.3}^x} + {3^{ - x}}} \right)^{3{{\log }_3}\left( {x - 1} \right) - {{\log }_3}\left( {x - 1} \right)\left( {2x + 1} \right)}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\log _2^2\left( {2 + x - {x^2}} \right) + 3{\log _{\frac{1}{2}}}\left( {2 + x - {x^2}} \right) + 2 \le 0\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\log _{x + 1}}{\left( {{x^2} + x - 6} \right)^2} \ge 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
3)\,\,\,{\log _{9{x^2}}}\left( {6 + 2x - {x^2}} \right) \le \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)\\
4)\,\,\,{9^{\sqrt {{x^2} - 3} }} + 3 <28. {3^{\sqrt {{x^2} - 3} - 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(4)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,{\log _{\frac{1}{{\sqrt 5 }}}}\left( {{6^{x + 1}} - {{36}^x}} \right) \ge - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,{\log _{\frac{1}{{\sqrt 6 }}}}\left( {{5^{x + 1}} - {{25}^x}} \right) \ge - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1){\left( {{x^2} + x + 1} \right)^x} < 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2){\left( {x - 1} \right)^{{x^2} - 6x + 8}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,{\left( {\sqrt 2 + 1} \right)^{\frac{{6x - 6}}{{x + 1}}}} \le {\left( {\sqrt 2 - 1} \right)^{ - x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\left( {\sqrt 5 + 2} \right)^{x - 1}} \ge {\left( {\sqrt 5 - 2} \right)^{\frac{{x - 1}}{{x + 1}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\,
\end{array}$
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