Tìm tất cả các tham số thực m > 1 để phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMzfvLHfij5gC1rhimfMBNvxyNvga7XvAUrhxSL % wBPr3CFThm951ET13ECXwzMrhkGidETediCjxANHgDPWfDLHhD7rwF % 41xp7ThE951EY0xFTmdERqtFamXvP5wqSXMqHnxAJn0BKvguHDwzZb % qefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9fr % Fj0-OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVg % Fr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa % aaaaaaa8qadaWdXbWdaeaapeWaaeWaa8aabaWdbiaaikdacaWG4bGa % eyOeI0IaaGymaaGaayjkaiaawMcaaiaabsgacaWG4baal8aabaWdbi % aaicdaa8aabaWdbiaad2gaa0Gaey4kIipakiabg2da9iaadIhapaWa % aWbaaSqabeaapeGaaGOmaaaakiabgkHiTiaaiodacaWG4bGaey4kaS % IaaGinaaaa!6951! \int\limits_0^m {\left( {2x - 1} \right){\rm{d}}x} = {x^2} - 3x + 4\) có hai nghiệm phân biệt?
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape % Waa8qCa8aabaWdbmaabmaapaqaa8qacaaIYaGaamiEaiabgkHiTiaa % igdaaiaawIcacaGLPaaacaqGKbGaamiEaaWcpaqaa8qacaaIWaaapa % qaa8qacaWGTbaaniabgUIiYdGccqGH9aqpcaWG4bWdamaaCaaaleqa % baWdbiaaikdaaaGccqGHsislcaaIZaGaamiEaiabgUcaRiaaisdacq % GHuhY2caWG4bWdamaaCaaaleqabaWdbiaaikdaaaGccqGHsislcaaI % ZaGaamiEaiabgUcaRiaaisdacqGHsislcaWGTbWdamaaCaaaleqaba % WdbiaaikdaaaGccqGHRaWkcaWGTbGaeyypa0JaaGimaaaa!5805! \int\limits_0^m {\left( {2x - 1} \right){\rm{d}}x} = {x^2} - 3x + 4 \Leftrightarrow {x^2} - 3x + 4 - {m^2} + m = 0\)
Phương trình có hai nghiệm phân biệt \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape % GaeuiLdqKaeyypa0JaaGinaiaad2gapaWaaWbaaSqabeaapeGaaGOm % aaaakiabgkHiTiaaisdacaWGTbGaeyOeI0IaaG4naiabg6da+iaaic % dacqGHuhY2daWabaWdaqaabeqaa8qacaWGTbGaeyipaWZaaSaaa8aa % baWdbiaaigdacqGHsislcaaIYaWaaOaaa8aabaWdbiaaikdaaSqaba % aak8aabaWdbiaaikdaaaaapaqaa8qacaWGTbGaeyOpa4ZaaSaaa8aa % baWdbiaaigdacqGHRaWkcaaIYaWaaOaaa8aabaWdbiaaikdaaSqaba % aak8aabaWdbiaaikdaaaaaaiaawUfaaaaa!51A1! \Delta = 4{m^2} - 4m - 7 > 0 \Leftrightarrow \left[ \begin{array}{l} m < \frac{{1 - 2\sqrt 2 }}{2}\\ m > \frac{{1 + 2\sqrt 2 }}{2} \end{array} \right.\)
Mà theo giả thiết m > 1 nên giá trị cần tìm là m > 2