Toán So sánh \({\left( {{{20}^{2016}} + {{11}^{2016}}} \right)^{2017}}\,\,\& \,\,{\left( {{{20}^{2017}} + {{11}^{2017}}} \right)^{2016}}\) 22/07/2021 By Kinsley So sánh \({\left( {{{20}^{2016}} + {{11}^{2016}}} \right)^{2017}}\,\,\& \,\,{\left( {{{20}^{2017}} + {{11}^{2017}}} \right)^{2016}}\)
$(20^{2016}+11^{2016})^{2017}$ $= (20^{2016}+11^{2016})^{2016}.(20^{2016}+11^{2016})$ $> (20^{2016}+11^{2016})^{2016}.20^{2016}$ $= (20.20^{2016}+20.11^{2016})^{2016}$ $> (20.20^{2016}+11.11^{2016})^{2016}$ $= (20^{2017}+11^{2017})^{2016}$ Vậy $(20^{2016}+11^{2016})^{2017}>(20^{2017}+11^{2017})^{2016}$ Trả lời
Đáp án: `(20^2016 + 11^2016)^2017 > (20^2017 + 11^2017)^2016` Giải thích các bước giải: Đặt `A = (20^2016 + 11^2016)^2017` và `B = (20^2017 + 11^2017)^2016` Ta có: `A = (20^2016 + 11^2016)^2017` `= (20^2016 + 11^2016)^2016 . (20^2016 + 11^2016)` `> (20^2016 + 11^2016)^2016 . 20^2016 = ((20^2016 + 11^2016) . 20)^2016` `= (20^2017 + 20 . 11^2016)^2016 > (20^2017 + 11 . 11^2016)^2016` `= (20^2017 + 11^2017)^2016` `⇒ A > B` `⇒ (20^2016 + 11^2016)^2017 > (20^2017 + 11^2017)^2016` Vậy `(20^2016 + 11^2016)^2017 > (20^2017 + 11^2017)^2016` Trả lời