So sánh : `A = ( 2020^2019 + 2019^2019 )^2020` và `B = ( 2020^2020 + 2019^2020 )^2019`

0 bình luận về “So sánh : `A = ( 2020^2019 + 2019^2019 )^2020` và `B = ( 2020^2020 + 2019^2020 )^2019`”

1. Đáp án:

    

   B=(2019^2020+2020^2020)^2019

   = ( 2019^2019 × 2019 + 2020^ 2019 ×2020) ^2019 
   A=(2019^2019+2020^2019)^2020
   = ( 2019 ^2019 + 2020 ^2019) ^ 2019 × (2019^2019 + 2020^2019)
   B / A = ( 2019^2019 × 2019 + 2020^ 2019 ×2020) ^2019  / ( 2019 ^2019 + 2020 ^2019) ^ 2019 × (2019^2019 + 2020^2019)
   = 2019 + 2020 / (2019^2019 + 2020^2019)
   ⇒ A lớn hơn B

   Bình luận

2. `*)A=(2019^{2019}+2020^{2019})^{2020}`
   `=(2019^{2019}+2020^{2019})^{2019}.(2019^{2019}+2020^{2019})`

   `*)B=(2019^2020+2020^2020)^2019`

   `=(2019^{2019}.2019+2020^{2019}.2020)^{2019}`

   `B/A={(2019^{2019}.2019+2020^{2019}.2020)^{2019}}/{(2019^{2019}+2020^{2019})^{2019}.(2019^{2019}+2020^{2019})}`
   `={2019+2020}/{2019^{2019}+2020^{2019}}`
   `->A>B(đpcm)`     

   xin hay nhất

   Bình luận