Question

[Lâm Huyên]

So sánh

A= 4(3²+1)(3⁴+1)(3⁸+1).....(3⁶⁴+1) và B=3¹²⁶-1

p/s: Mìh cần gấp lắm nha^^bạn nào bk giúp mìh

Answer 1

[kagamine rin len]

A=4(3^2+1)(3^4+1)(3^8+1)...(3^64+1)

2A=8(3^2+1)(3^4+1)(3^8+1)...(3^64+1)

2A=(3^2-1)(3^2+1)(3^4+1)(3^8+1)...(3^64+1)

2A=(3^4-1)(3^4+1)(3^8+1)...(3^64+1)

2A=(3^8-1)(3^8+1)....(3^64+1)

2A=(3^16-1)...(3^64+1)

......

2A=(3^64-1)(3^64+1)

2A=3^128-1

A=(3^128-1)/2

=> A>B

Answer 2

[Mai Thành Đạt]

\(A=4\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^2-1\right)\left(3^2+1\right)...\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^8-1\right)\left(3^8+1\right)...\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^{16}-1\right)\left(3^{16}+1\right)...\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^{32}-1\right)\left(3^{32}+1\right)\left(3^{64}+1\right)\)

\(\Leftrightarrow4A=\left(3^{64}-1\right)\left(3^{64}+1\right)\Leftrightarrow4A=3^{128}-1\Leftrightarrow A=\frac{3^{128}-1}{4}\)

Ta có \(\frac{3^{128}-1}{4}< 3^{128}-1\Rightarrow A< B\)

Lâm Huyền:Bạn sai đề rồi B phải là 3¹²⁸-1 chứ !