` a) ` Ta có:
` B = 2020^{2} `
` <=> B = 2020.2020 `
Do: ` 2019 < 2020 `
` <=> 2019.2020 < 2020.2020 `
` <=> 2019.2020 < 2020^{2} `
` <=> A < B `
` b) ` Ta có:
` A=(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=2(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=(3-1)(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=(3^2-1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=(3^4-1)(3^4 + 1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=(3^8-1)(3^8 + 1)(3^{16} + 1) `
` <=> 2A=(3^{16}-1)(3^{16}+ 1) `
` <=> 2A=3^{32} - 1 `
Mà ` B = 3^{32} - 1 `
` => 2A = B `
` => A<B `
