Tìm số hạng không chứa x trong khai triển nhị thức Newton \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca % WG4bGaeyOeI0YaaSaaaeaacaaIYaaabaGaamiEamaaCaaaleqabaGa % aGOmaaaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaaikdacaaIXa % aaaaaa!3DC6! {\left( {x - \frac{2}{{{x^2}}}} \right)^{21}}\), \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca % WG4bGaeyiyIKRaaGimaiaacYcacaaMc8UaaGPaVlaad6gacqGHiiIZ % cqWIvesPdaahaaWcbeqaaiaacQcaaaaakiaawIcacaGLPaaaaaa!4388! \left( {x \ne 0,\,\,n \in {N^*}} \right)\).
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Lời giải:
Báo saiTa có : \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaDa % aaleaacaWGUbaabaGaam4AaaaakiaadggadaahaaWcbeqaaiaad6ga % cqGHsislcaWGRbaaaOGaamOyamaaCaaaleqabaGaam4Aaaaakiabg2 % da9iaadoeadaqhaaWcbaGaaGOmaiaaigdaaeaacaWGRbaaaOGaamiE % amaaCaaaleqabaGaaGOmaiaaigdacqGHsislcaWGRbaaaOGaaiOlam % aabmaabaGaeyOeI0YaaSaaaeaacaaIYaaabaGaamiEamaaCaaaleqa % baGaaGOmaaaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaadUgaaa % GccqGH9aqpdaqadaqaaiabgkHiTiaaikdaaiaawIcacaGLPaaadaah % aaWcbeqaaiaadUgaaaGccaWGdbWaa0baaSqaaiaaikdacaaIXaaaba % Gaam4AaaaakiaadIhadaahaaWcbeqaaiaaikdacaaIXaGaeyOeI0Ia % aG4maiaadUgaaaaaaa!5CCF!\ C_n^k{a^{n - k}}{b^k} = C_{21}^k{x^{21 - k}}.{\left( { - \frac{2}{{{x^2}}}} \right)^k} = {\left( { - 2} \right)^k}C_{21}^k{x^{21 - 3k}}\)
Theo yêu cầu bài toán \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaaG % OmaiaaigdacqGHsislcaaIZaGaam4Aaiabg2da9iaaicdacqGHuhY2 % caWGRbGaeyypa0JaaG4naaaa!4333! \Leftrightarrow 21 - 3k = 0 \Leftrightarrow k = 7\). Vậy hệ số cần tìm là .\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG % OmamaaCaaaleqabaGaaG4naaaakiaadoeadaqhaaWcbaGaaGOmaiaa % igdaaeaacaaI3aaaaaaa!3BC1! - {2^7}C_{21}^7\)
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
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