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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: So sánh `A=(20^2021+11^2021)^2022` và `B=(20^2022+11^2022)^2021`

Toán Lớp 9: So sánh
A=(20^2021+11^2021)^2022 và B=(20^2022+11^2022)^2021

Comments ( 2 )

  1. A=(20^(2021)+11^(2021))^2022
    A=(20^(2021)+11^(2021)).(20^(2021)+11^(2021))^2021
    A=(20^(2021+2021)+20^(2021).11^(2021)+20^(2021).11^(2021)+11^(2021+2021))^2021
    A=(20^(4042)+2(20^(2021).11^(2021))+11^(4042))^2021
    Mà (20^(4042)+2(20^(2021).11^(2021))+11^(4042))^2021>(20^(2022)+11^(2022))^2021
    Vậy A>B
     

  2. A = (20^2021 + 11^2021)^2022
    = (20^2021 + 11^2021).(20^2021 + 11^2021)^2021
    =(20^(2021+2021) +20^2021 .11^2021+20^2021 .11^2021+11^(2021+2021)^2021
    =(20^2042 + 2(20^2021 .11^2021)+11^2042)^2021
    mặt khác (20^2042 + 2(20^2021 .11^2021)+11^2042)^2021 > (20^2022 + 11^2022)^2021 =B
    Vậy A > B

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222-9+11+12:2*14+14 = ? ( )