Tìm tất cả các giá trị thực của tham số m để bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaaI3aGaamiE % amaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaiEdaaiaawIcacaGLPa % aacqGHLjYSciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGc % daqadaqaaiaad2gacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaS % IaaGinaiaadIhacqGHRaWkcaWGTbaacaGLOaGaayzkaaGaaiilaiaa % bccacqGHaiIicaWG4bGaeyicI4SaeSyhHeQaaiOlaaaa!54BD! {\log _2}\left( {7{x^2} + 7} \right) \ge {\log _2}\left( {m{x^2} + 4x + m} \right),{\rm{ }}\forall x \in R .\)

Bất phương trình tương đương \( 7{x^2} + 7 \ge m{x^2} + 4x + m > 0,{\rm{ }}\forall x \in R\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaamaabmaabaGaaG4naiabgkHiTiaad2gaaiaawIcacaGL % PaaacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGinaiaadI % hacqGHRaWkcaaI3aGaeyOeI0IaamyBaiabgwMiZkaaicdacaqGGaGa % aeiiaiaabccacaGGOaGaaGOmaiaacMcaaeaacaWGTbGaamiEamaaCa % aaleqabaGaaGOmaaaakiabgUcaRiaaisdacaWG4bGaey4kaSIaamyB % aiabg6da+iaaicdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc % cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii % aiaabccacaqGGaGaaeiiaiaacIcacaaIZaGaaiykaaaacaGL7baaca % GGSaGaaeiiaiabgcGiIiaadIhacqGHiiIZcqWIDesOaaa!6844! \Leftrightarrow \left\{ \begin{array}{l} \left( {7 - m} \right){x^2} - 4x + 7 - m \ge 0{\rm{ }}(2)\\ m{x^2} + 4x + m > 0{\rm{ }}(3) \end{array} \right.,{\rm{ }}\forall x \in R\)

m = 7 : (2) không thỏa \(\forall x \in R\)

m = 0 : (3) không thỏa \(\forall x \in R\)

(1) thỏa \(\forall x \in R\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaaiEdacqGHsislcaWGTbGaeyOpa4JaaGimaaqaaiqb % gs5aezaafaWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0JaaGinaiabgk % HiTmaabmaabaGaaG4naiabgkHiTiaad2gaaiaawIcacaGLPaaadaah % aaWcbeqaaiaaikdaaaGccqGHKjYOcaaIWaaabaGaamyBaiabg6da+i % aaicdaaeaacuGHuoargaqbamaaBaaaleaacaaIZaaabeaakiabg2da % 9iaaisdacqGHsislcaWGTbWaaWbaaSqabeaacaaIYaaaaOGaeyipaW % JaaGimaaaacaGL7baacaqGGaGaaeiiaiaabccacqGHuhY2caqGGaGa % aeiiamaaceaaeaqabeaacaWGTbGaeyipaWJaaG4naaqaaiaad2gacq % GHKjYOcaaI1aaabaGaamyBaiabg6da+iaaicdaaeaacaWGTbGaeyOp % a4JaaGOmaaaacaGL7baacaqGGaGaaeiiaiabgsDiBlaabccacaqGGa % GaaGOmaiabgYda8iaad2gacqGHKjYOcaaI1aGaaiOlaaaa!72D9! \Leftrightarrow \left\{ \begin{array}{l} 7 - m > 0\\ {{\Delta '}_2} = 4 - {\left( {7 - m} \right)^2} \le 0\\ m > 0\\ {{\Delta '}_3} = 4 - {m^2} < 0 \end{array} \right.{\rm{ }} \Leftrightarrow {\rm{ }}\left\{ \begin{array}{l} m < 7\\ m \le 5\\ m > 0\\ m > 2 \end{array} \right.{\rm{ }} \Leftrightarrow {\rm{ }}2 < m \le 5.\)