Có: \(A=4\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

          \(=\frac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

           \(=\frac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

          \(=...........................\)

           \(=\frac{3^{32}-1}{2}\)

\(B=3^{32-1}\)

=> \(A< B\)

Nó hơi dài cậu chờ tí nka !

Mình ghi nhầm đề bài 1 tí đề bài là :

So sánh 2 số A và B biết : 

A = (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1) và B = 3^32 - 1

A = (2-1)(2+1)(2^2 + 1 ) (2^4 + 1 ) ( 2^8 + 1) ( 2^16 + 1)

A = (2^2 - 1)(2^2 + 1 ) ( 2^4 + 1 )(2^8 + 1 )(2^16 + 1) 

A= ( 2^4 - 1 )( 2^4 + 1 )(2^8 + 1 )(2^16 + 1 )

A = (2^8 - 1 )(2^8 + 1 )(2^16 + 1 )

A = (2^16 - 1 )(2^16 + 1 )

A =  2^32 - 1 < 2^32 = B
Vậy A = B
k mik nka !

\(A=4.\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^{16}-1\right)\left(3^{16}+1\right)\)

\(=\frac{3^{32}-1}{2}< 3^{32}-1=B\)

Vậy \(A< B\)

A= 80.(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

A = (3⁴ - 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

A = (3⁸ - 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

A = (3¹⁶ - 1)(3¹⁶ + 1)(3³² + 1)

A = (3³² - 1)(3³² + 1)

A = 3⁶⁴ - 1 < 3⁶⁴ = B

=> A < B

nhầm tớ lộn sang bài khác sorry

trình bày cách giải giùm với nhé

a) A = 2016.2018 = ( 2017 - 1 ).2018 = 2017.2018 - 2018 ( 1 )

B = 2017² = 2017.2017 = 2017.( 2018 - 1) = 2017.2018 - 2017 ( 2 )

Từ (1) và (2), ta thấy: - 2018 < - 2017 => 2017.2018 - 2018 < 2017.2018 - 2017 <=> 2016.2018 < 2017²

Vậy A < B 

~ Phần b khi nào nghĩ ra tớ sẽ làm ngay ạ :) Còn phần này chắc chắn đúng cậu nhé ~

b)\(x=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(2x=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(2x=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(2x=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(2x=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(2x=\left(3^{16}-1\right)\left(3^{16}+1\right)\Rightarrow x=\frac{3^{32}-1}{2}\)

Thấy \(x=\frac{3^{32-1}}{2}< 3^{32}-1=y\)