Tập hợp tất cả các giá trị thực của tham số m để đường thẳng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iabgkHiTiaaikdacaWG4bGaey4kaSIaamyBaaaa!3C71! y = - 2x + m\) cắt đồ thị của hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaamiEaiabgUcaRiaaigdaaeaacaWG4bGaeyOeI0Ia % aGOmaaaaaaa!3D47! y = \frac{{x + 1}}{{x - 2}}\) tại hai điểm phân biệt là.
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Lời giải:
Báo saiĐiều kiện: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgc % Mi5kaaikdaaaa!3973! x \ne 2\)
Phương trình hoành độ giao điểm : \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WG4bGaey4kaSIaaGymaaqaaiaadIhacqGHsislcaaIYaaaaiabg2da % 9iabgkHiTiaaikdacaWG4bGaey4kaSIaamyBaiabgsDiBlaaikdaca % WG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0YaaeWaaeaacaWGTbGa % ey4kaSIaaG4maaGaayjkaiaawMcaaiaadIhacqGHRaWkcaaIYaGaam % yBaiabgUcaRiaaigdacqGH9aqpcaaIWaWaaeWaaeaacaGGQaaacaGL % OaGaayzkaaaaaa!53F3! \frac{{x + 1}}{{x - 2}} = - 2x + m \Leftrightarrow 2{x^2} - \left( {m + 3} \right)x + 2m + 1 = 0\left( * \right)\)
Theo yêu cầu bài toán \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aae % WaaeaacaGGQaaacaGLOaGaayzkaaaaaa!3A86! \Leftrightarrow \left( * \right)\) có hai nghiệm phân biệt khác 2.
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaamaabmaabaGaamyBaiabgUcaRiaaiodaaiaawIcacaGL % PaaadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaI0aGaaiOlaiaaik % dadaqadaqaaiaaikdacaWGTbGaey4kaSIaaGymaaGaayjkaiaawMca % aiabg6da+iaaicdaaeaacaaI4aGaeyOeI0IaaGOmamaabmaabaGaam % yBaiabgUcaRiaaiodaaiaawIcacaGLPaaacqGHRaWkcaaIYaGaamyB % aiabgUcaRiaaigdacqGHGjsUcaaIWaaaaiaawUhaaaaa!555F! \Leftrightarrow \left\{ \begin{array}{l} {\left( {m + 3} \right)^2} - 4.2\left( {2m + 1} \right) > 0\\ 8 - 2\left( {m + 3} \right) + 2m + 1 \ne 0 \end{array} \right.\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaad2gadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaI % XaGaaGimaiaad2gacqGHRaWkcaaIXaGaeyOpa4JaaGimaaqaaiaaio % dacqGHGjsUcaaIWaaaaiaawUhaaiabgsDiBlaad2gacqGH8aapcaaI % 1aGaeyOeI0IaaGOmamaakaaabaGaaGOnaaWcbeaaaaa!4CDB! \Leftrightarrow \left\{ \begin{array}{l} {m^2} - 10m + 1 > 0\\ 3 \ne 0 \end{array} \right. \Leftrightarrow m < 5 - 2\sqrt 6 \ \)hoặc \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabg6 % da+iaaiwdacqGHRaWkcaaIYaWaaOaaaeaacaaI2aaaleqaaaaa!3B25! m > 5 + 2\sqrt 6 \).
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
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