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27 tháng 12 2016

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

\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)=\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^{32}-1\right)\left(3^{32}+1\right)=3^{64}-1\)

25 tháng 9 2021

a) \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^{32}-1\right)< 3^{32}-1=B\)

b) \(A=2011.2013=\left(2012-1\right)\left(2012+1\right)=2012^2-1< 2012^2=B\)

15 tháng 10 2023

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

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

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

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

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

\(=\dfrac{1}{2}\left(3^{32}-1\right)\)

22 tháng 10 2020

a) Ta có : 2005.2007 = (2006 - 1)(2006 + 1) = 20062 - 12 = 20062 - 1 ( cái khúc này sửa : 2005.2001 thành 2005.2007)

Mà B = 20062

=> 20062 - 1 < 20062 

=> A < B

b) Ta có : B = (2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)

                B =  (2 - 1)(2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)

                B = (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)

                B = (24 - 1)(24 + 1)(28 + 1)(216 + 1)

                B = (28 - 1)(28 + 1)(216 + 1) = (216 - 1)(216 + 1) = 232 - 1

Mà C = 232

=> B < C 

c) Tương tự như câu b

12 tháng 9 2021

\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}.\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^{32}-1\right)=\dfrac{3^{32}}{2}-\dfrac{1}{2}\)

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

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

\(=\dfrac{3^{32}-1}{2}\)

DT
8 tháng 11 2023

\(A=8.\left(3^2+1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^4-1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^8-1\right)....\left(3^{16}+1\right)\\ =\left(3^{16}-1\right)\left(3^{16}+1\right)\\ =3^{32}-1\)

8 tháng 11 2023

A = 8.(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3² - 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3⁴ - 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3⁸ - 1)(3⁸ + 1)(3¹⁶ + 1)

= (3¹⁶ - 1)(3¹⁶ + 1)

= 3³² - 1

17 tháng 6 2018

29 tháng 3 2022

yggucbsgfuyvfbsudy

30 tháng 3 2022

????????

18 tháng 7 2021

cho mình cảm ơn nhiều nha!

 

6 tháng 2 2023

Các bước giải chi tiết 

a)  \(\dfrac{392-x}{32}\) + \(\dfrac{390-x}{34}\) + \(\dfrac{388-x}{36}\) = -3

⇔ \(\dfrac{392-x}{32}\)+1+\(\dfrac{390-x}{34}\)+1+\(\dfrac{388-x}{36}\)+1 = 0 

\(\dfrac{424-x}{32}\)+\(\dfrac{424-x}{34}\)+\(\dfrac{424-x}{36}\)=0

\(\left(424-x\right)\)\(\left(\dfrac{1}{32}+\dfrac{1}{34}+\dfrac{1}{36}\right)\)=0

\(424-x\) = 0\(\left(\dfrac{1}{32}+\dfrac{1}{34}+\dfrac{1}{36}\ne\forall x\right)\)

\(x=424\)

b)  \(\dfrac{x-3}{3}\)\(x\) = \(5-\dfrac{x+1}{4}\)

\(\dfrac{x-3-3x}{3}\) = 5 + \(\dfrac{-\left(x+1\right)}{4}\)

\(\dfrac{-2x-3}{3}\) = 5 + \(\dfrac{-x-1}{4}\)

\(\dfrac{-2x-3}{3}\) = \(\dfrac{20-x-1}{4}\)

\(\dfrac{-2x-3}{3}\) = \(\dfrac{-x+19}{4}\)

⇔ \(4\left(-2x-3\right)\) = \(3\left(-x+19\right)\)

\(-8x-12\) = \(-3x+57\)

\(-8x\) = \(-3x+69\)

\(-5x=69\)

⇔ \(x=-\dfrac{69}{5}\)

6 tháng 2 2023

(392-x)/32+(390-x)/34+(388-x)/36=-3
=>392-x)/32 +1 + (390-x)/34 +1 +(388-x)/36 +1=0
=>(424-x)/32+(424-x)/34+(424-x)/36=0
=>424-x=0(vì 1/32+1/34+1/36 khác 0)
=>x=424