So sánh \({\left( {{{20}^{2016}} + {{11}^{2016}}} \right)^{2017}}\,\,\& \,\,{\left( {{{20}^{2017}} + {{11}^{2017}}} \right)^{2016}}\)
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 $(20^{2016}+11^{2016})^{2017}>(20^{2017}+11^{2017})^{2016}$
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`