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