Tìm nghiệm nguyên nhỏ nhất của bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaiodaaeqaaOWaaeWaaeaacaaIXaGaeyOe % I0IaamiEamaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaiabgs % MiJkGacYgacaGGVbGaai4zamaaBaaaleaadaWcaaqaaiaaigdaaeaa % caaIZaaaaaqabaGcdaqadaqaaiaaigdacqGHsislcaWG4baacaGLOa % Gaayzkaaaaaa!4949! {\log _3}\left( {1 - {x^2}} \right) \le {\log _{\frac{1}{3}}}\left( {1 - x} \right)\)

Ta có: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaiodaaeqaaOWaaeWaaeaacaaIXaGaeyOe % I0IaamiEamaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaiabgs % MiJkGacYgacaGGVbGaai4zamaaBaaaleaadaWcaaqaaiaaigdaaeaa % caaIZaaaaaqabaGcdaqadaqaaiaaigdacqGHsislcaWG4baacaGLOa % GaayzkaaGaeyi1HSTaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaioda % aeqaaOWaaeWaaeaacaaIXaGaeyOeI0IaamiEamaaCaaaleqabaGaaG % OmaaaaaOGaayjkaiaawMcaaiabgsMiJkGacYgacaGGVbGaai4zamaa % BaaaleaacaaIZaaabeaakmaalaaabaGaaGymaaqaaiaaigdacqGHsi % slcaWG4baaaiabgsDiBpaaceaaeaqabeaacaaIXaGaeyOeI0IaamiE % amaaCaaaleqabaGaaGOmaaaakiabg6da+iaaicdaaeaacaaIXaGaey % OeI0IaamiEamaaCaaaleqabaGaaGOmaaaakiabgsMiJoaalaaabaGa % aGymaaqaaiaaigdacqGHsislcaWG4baaaaaacaGL7baacqGHuhY2da % GabaabaeqabaGaeyOeI0IaaGymaiabgYda8iaadIhacqGH8aapcaaI % XaaabaWaaSaaaeaacaWG4bWaaWbaaSqabeaacaaIZaaaaOGaeyOeI0 % IaamiEamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaadIhaaeaacaaI % XaGaeyOeI0IaamiEaaaacqGHKjYOcaaIWaaaaiaawUhaaaaa!83C6! {\log _3}\left( {1 - {x^2}} \right) \le {\log _{\frac{1}{3}}}\left( {1 - x} \right) \Leftrightarrow {\log _3}\left( {1 - {x^2}} \right) \le {\log _3}\frac{1}{{1 - x}} \Leftrightarrow \left\{ \begin{array}{l} 1 - {x^2} > 0\\ 1 - {x^2} \le \frac{1}{{1 - x}} \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} - 1 < x < 1\\ \frac{{{x^3} - {x^2} - x}}{{1 - x}} \le 0 \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaaiabgkHiTiaaigdacqGH8aapcaWG4bGaeyipaWJaaGymaaqaaiaa % dIhadaahaaWcbeqaaiaaiodaaaGccqGHsislcaWG4bWaaWbaaSqabe % aacaaIYaaaaOGaeyOeI0IaamiEaiabgsMiJkaaicdaaaGaay5EaaGa % eyi1HS9aaiqaaqaabeqaaiabgkHiTiaaigdacqGH8aapcaWG4bGaey % ipaWJaaGymaaqaamaadeaaeaqabeaacaWG4bGaeyizIm6aaSaaaeaa % caaIXaGaeyOeI0YaaOaaaeaacaaI1aaaleqaaaGcbaGaaGOmaaaaae % aacaaIWaGaeyizImQaamiEaiabgsMiJoaalaaabaGaaGymaiabgUca % RmaakaaabaGaaGynaaWcbeaaaOqaaiaaikdaaaaaaiaawUfaaaaaca % GL7baacqGHuhY2daWabaabaeqabaGaeyOeI0IaaGymaiabgYda8iaa % dIhacqGHKjYOdaWcaaqaaiaaigdacqGHsisldaGcaaqaaiaaiwdaaS % qabaaakeaacaaIYaaaaaqaaiaaicdacqGHKjYOcaWG4bGaeyipaWJa % aGymaaaacaGLBbaaaaa!6F42! \left\{ \begin{array}{l} - 1 < x < 1\\ {x^3} - {x^2} - x \le 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} - 1 < x < 1\\ \left[ \begin{array}{l} x \le \frac{{1 - \sqrt 5 }}{2}\\ 0 \le x \le \frac{{1 + \sqrt 5 }}{2} \end{array} \right. \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} - 1 < x \le \frac{{1 - \sqrt 5 }}{2}\\ 0 \le x < 1 \end{array} \right.\)

Vậy nghiệm nguyên nhỏ nhất là x = 0.