Question

So sánh:

A = 8 . (3²+1). (3⁴+1). ... .(3⁶⁴+1) với B = 3¹²⁸-1

Answer 1

Xét biểu thức A

\(A=8\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)

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

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

\(...=\left(3^{64}-1\right)\left(3^{64}+1\right)=3^{128}-1\)

Vậy \(A=B\)