so sánh 6^2020 +1/6^2021 -5 và 6^2021 +1/6^2022-5

Đặt $A=\dfrac{6^{2020}+1}{6^{2021}-5}$

$=>6A=\dfrac{6^{2021}-5+11}{6^{2021}-5}$

$=>6A=1+\dfrac{11}{6^{2021}-5}$

Đặt $B=\dfrac{6^{2021}+1}{6^{2022}-5}$

$=>6B=\dfrac{6^{2022}-5+11}{6^{2022}-5}$

$=>6B=1+\dfrac{11}{6^{2022}-5}$

Do $6^{2021}-5<6^{2022}-5$

$=>1+\dfrac{11}{6^{2021}-5}>1+\dfrac{11}{6^{2022}-5}$

$=>6A>6B$

$=>A>B$

Đáp án:

Đặt  `A = ( 6^2020 + 1 ) / ( 6^2021 - 5 )`

`->` `6A = ( 6^2021 + 6 ) / ( 6^2021 - 5 )`

`->` `6A = [ ( 6^2021 - 5 ) + 11 ] / ( 6^2021 - 5 )`

`->` `6A = ( 6^2021 - 5 ) / ( 6^2021 - 5 ) + 11 / ( 6^2021 - 5 )`

`->` `6A = 1 + 11 / ( 6^2021 - 5 )`

Đặt  `B = ( 6^2021 + 1 ) / ( 6^2022 - 5 )`

`->` `6B = ( 6^2022 + 6 ) / ( 6^2022 - 5 )`

`->` `6B = [ ( 6^2022 - 5 ) + 11 ] / ( 6^2022 - 5 )`

`->` `6B = ( 6^2022 - 5 ) / ( 6^2022 - 5 ) + 11 / ( 6^2022 - 5 )`

`->` `6B = 1 + 11 / ( 6^2022 - 5 )`

Mà  `11 / ( 6^2021 - 5 ) > 1 / ( 6^2022 - 5 )`  `(` vì  `6^2022 - 5 > 6^2021 - 5` `)`

`->` `1 + 11 / ( 6^2021 - 5 ) > 1 + 1 / ( 6^2022 - 5 )`

`->` `6A > 6B`

`->` `A > B`

Vậy  `( 6^2020 +1)/(6^2021 -5) > (6^2021 +1)/(6^2022-5)`.