Evaluate (3+1)(32+1)(34+1)(38+1)(316+1)(332+1).

Question by Cristiano Ronaldo

19/03/2017 at 11:36

rational numbers

FA KAKALOTS 03/02/2018 at 12:43

Let A = (3 + 1)(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)

=> 2A = (3 - 1)(3 + 1)(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)

= (32 - 1)(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)

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

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

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

= (332 - 1)(332 + 1)

= 364 - 1

⇒A=364−12
Phan Thanh Tinh Coordinator 22/03/2017 at 22:30

Let A = (3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

=> 2A = (3 - 1)(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

= (3² - 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶+ 1)(3³² + 1)

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

= (3⁸ - 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

= (3¹⁶ - 1)(3¹⁶ + 1)(3³² + 1)

= (3³² - 1)(3³² + 1)

= 3⁶⁴ - 1

\(\Rightarrow A=\dfrac{3^{64}-1}{2}\)
Phan Huy Toàn 15/08/2017 at 08:36

bạn không nên đăng những câu hỏi linh tinh như 1+1,... trên diễn đàn