Tìm m để bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgU % caRiGacYgacaGGVbGaai4zamaaBaaaleaacaaI1aaabeaakmaabmqa % baGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaigdaaiaawI % cacaGLPaaacqGHLjYSciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGyn % aaqabaGcdaqadeqaaiaad2gacaWG4bWaaWbaaSqabeaacaaIYaaaaO % Gaey4kaSIaaGinaiaadIhacqGHRaWkcaWGTbaacaGLOaGaayzkaaaa % aa!4ED5! 1 + {\log _5}\left( {{x^2} + 1} \right) \ge {\log _5}\left( {m{x^2} + 4x + m} \right)\) thoã mãn với mọi \(x\in R\)

BPT thỏa mãn với mọi \(x \in R \iff \left\{ \begin{array}{l} m{x^2} + 4x + m > 0\\ 5\left( {{x^2} + 1} \right) \ge m{x^2} + 4x + m \end{array} \right.\left( {\forall x \in R } \right)\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqabqaabe % qaaiaad2gacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGin % aiaadIhacqGHRaWkcaWGTbGaeyOpa4JaaGimaaqaamaabmqabaGaaG % ynaiabgkHiTiaad2gaaiaawIcacaGLPaaacaWG4bWaaWbaaSqabeaa % caaIYaaaaOGaeyOeI0IaaGinaiaadIhacqGHRaWkcaaI1aGaeyOeI0 % IaamyBaiabgwMiZkaaicdaaaGaay5EaaWaaeWabeaacqGHaiIicaWG % 4bGaeyicI4SaeSyhHekacaGLOaGaayzkaaaaaa!5536! \left\{ \begin{array}{l} m{x^2} + 4x + m > 0\\ \left( {5 - m} \right){x^2} - 4x + 5 - m \ge 0 \end{array} \right.\left( {\forall x \in R} \right)\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqabqaabe % qaaiaad2gacqGH+aGpcaaIWaaabaGaaGymaiaaiAdacqGHsislcaaI % 0aGaamyBamaaCaaaleqabaGaaGOmaaaakiabgYda8iaaicdaaeaaca % aI1aGaeyOeI0IaamyBaiabg6da+iaaicdaaeaacaaIXaGaaGOnaiab % gkHiTiaaisdadaqadeqaaiaaiwdacqGHsislcaWGTbaacaGLOaGaay % zkaaWaaWbaaSqabeaacaaIYaaaaOGaeyizImQaaGimaaaacaGL7baa % aaa!4FA5! \iff\left\{ \begin{array}{l} m > 0\\ 16 - 4{m^2} < 0\\ 5 - m > 0\\ 16 - 4{\left( {5 - m} \right)^2} \le 0 \end{array} \right.\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqabqaabe % qaaiaad2gacqGH+aGpcaaIWaaabaWaamqabqaabeqaaiaad2gacqGH % 8aapcqGHsislcaaIYaaabaGaamyBaiabg6da+iaaikdaaaGaay5waa % aabaGaamyBaiabgYda8iaaiwdaaeaadaWabeabaeqabaGaamyBaiab % gsMiJkaaiodaaeaacaWGTbGaeyyzImRaaG4naaaacaGLBbaaaaGaay % 5Eaaaaaa!4BB9! \iff\left\{ \begin{array}{l} m > 0\\ \left[ \begin{array}{l} m < - 2\\ m > 2 \end{array} \right.\\ m < 5\\ \left[ \begin{array}{l} m \le 3\\ m \ge 7 \end{array} \right. \end{array} \right.\)\(\iff % MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabgY % da8iaad2gacqGHKjYOcaaIZaaaaa!3B18! 2 < m \le 3\)