Bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaWG4bWaaWba % aSqabeaacaaIYaaaaOGaeyOeI0IaamiEaiabgkHiTiaaikdaaiaawI % cacaGLPaaacqGHLjYSciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGim % aiaacYcacaaI1aaabeaakmaabmaabaGaamiEaiabgkHiTiaaigdaai % aawIcacaGLPaaacqGHRaWkcaaIXaaaaa!4D82! {\log _2}\left( {{x^2} - x - 2} \right) \ge {\log _{0,5}}\left( {x - 1} \right) + 1\) có tập nghiệm là:

TXĐ: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaWG % 4bGaeyOeI0IaaGOmaiabg6da+iaaicdaaeaacaWG4bGaeyOeI0IaaG % ymaiabg6da+iaaicdaaaGaay5EaaGaeyi1HS9aaiqaaqaabeqaaiaa % dIhacqGH8aapcqGHsislcaaIXaGaeyikIOTaamiEaiabg6da+iaaik % daaeaacaWG4bGaeyOpa4JaaGymaaaacaGL7baacqGHuhY2caWG4bGa % eyOpa4JaaGOmaaaa!5890! \Leftrightarrow \left\{ \begin{array}{l} {x^2} - x - 2 > 0\\ x - 1 > 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x < - 1 \vee x > 2\\ x > 1 \end{array} \right. \Leftrightarrow x > 2\)

BPT\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaci % iBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaWG % 4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamiEaiabgkHiTiaaik % daaiaawIcacaGLPaaacqGHLjYSciGGSbGaai4BaiaacEgadaWgaaWc % baGaaGimaiaacYcacaaI1aaabeaakmaabmaabaGaamiEaiabgkHiTi % aaigdaaiaawIcacaGLPaaacqGHRaWkcaaIXaGaeyi1HSTaciiBaiaa % c+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaWG4bWaaW % baaSqabeaacaaIYaaaaOGaeyOeI0IaamiEaiabgkHiTiaaikdaaiaa % wIcacaGLPaaacqGHLjYSciGGSbGaai4BaiaacEgadaWgaaWcbaGaaG % OmamaaCaaameqabaGaeyOeI0IaaGymaaaaaSqabaGcdaqadaqaaiaa % dIhacqGHsislcaaIXaaacaGLOaGaayzkaaGaey4kaSIaaGymaaaa!6A3B! \Leftrightarrow {\log _2}\left( {{x^2} - x - 2} \right) \ge {\log _{0,5}}\left( {x - 1} \right) + 1 \Leftrightarrow {\log _2}\left( {{x^2} - x - 2} \right) \ge {\log _{{2^{ - 1}}}}\left( {x - 1} \right) + 1\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaci % iBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaWG % 4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamiEaiabgkHiTiaaik % daaiaawIcacaGLPaaacqGHRaWkciGGSbGaai4BaiaacEgadaWgaaWc % baGaaGOmaaqabaGcdaqadaqaaiaadIhacqGHsislcaaIXaaacaGLOa % GaayzkaaGaeyOeI0IaaGymaiabgwMiZkaaicdacqGHuhY2ciGGSbGa % ai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGcdaWcaaqaamaabmaaba % GaamiEamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaadIhacqGHsisl % caaIYaaacaGLOaGaayzkaaWaaeWaaeaacaWG4bGaeyOeI0IaaGymaa % GaayjkaiaawMcaaaqaaiaaikdaaaGaeyyzImRaaGimaaaa!64BB! \Leftrightarrow {\log _2}\left( {{x^2} - x - 2} \right) + {\log _2}\left( {x - 1} \right) - 1 \ge 0 \Leftrightarrow {\log _2}\frac{{\left( {{x^2} - x - 2} \right)\left( {x - 1} \right)}}{2} \ge 0\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aaS % aaaeaadaqadaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsisl % caWG4bGaeyOeI0IaaGOmaaGaayjkaiaawMcaamaabmaabaGaamiEai % abgkHiTiaaigdaaiaawIcacaGLPaaaaeaacaaIYaaaaiabgwMiZkaa % igdacqGHuhY2daqadaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccq % GHsislcaWG4bGaeyOeI0IaaGOmaaGaayjkaiaawMcaamaabmaabaGa % amiEaiabgkHiTiaaigdaaiaawIcacaGLPaaacqGHLjYScaaIYaGaey % i1HSTaamiEamaabmaabaGaamiEamaaCaaaleqabaGaaGOmaaaakiab % gkHiTiaaikdacaWG4bGaeyOeI0IaaGymaaGaayjkaiaawMcaaiabgw % MiZkaaicdaaaa!648E! \Leftrightarrow \frac{{\left( {{x^2} - x - 2} \right)\left( {x - 1} \right)}}{2} \ge 1 \Leftrightarrow \left( {{x^2} - x - 2} \right)\left( {x - 1} \right) \ge 2 \Leftrightarrow x\left( {{x^2} - 2x - 1} \right) \ge 0\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaam % iEamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaikdacaWG4bGaeyOe % I0IaaGymaiabgwMiZkaaicdacqGHuhY2daWabaabaeqabaGaamiEai % abgsMiJkaaigdacqGHsisldaGcaaqaaiaaikdaaSqabaGcdaqadaqa % aiaadYgacaWGVbGaamyyaiaadMgaaiaawIcacaGLPaaaaeaacaWG4b % GaeyyzImRaaGymaiabgUcaRmaakaaabaGaaGOmaaWcbeaakmaabmaa % baGaamiDaiaad2gaaiaawIcacaGLPaaaaaGaay5waaGaeyO0H4Taam % iEaiabgwMiZkaaigdacqGHRaWkdaGcaaqaaiaaikdaaSqabaaaaa!5F31! \Leftrightarrow {x^2} - 2x - 1 \ge 0 \Leftrightarrow \left[ \begin{array}{l} x \le 1 - \sqrt 2 \left( {loai} \right)\\ x \ge 1 + \sqrt 2 \left( {tm} \right) \end{array} \right. \Rightarrow x \ge 1 + \sqrt 2 \)