Question

So sánh A và B:

A=12(5²+1)(5⁴+1)............(5¹²⁸+1) và B=5²⁵⁶-1

Answer 1

\(\left(5^2-1\right)A=12\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right).\) ... .\(\left(5^{128}+1\right)\)

=\(12\left(5^4-1\right)\)\(\left(5^4+1\right)\)\(\left(5^8+1\right)\). ... .(5¹²⁸+1)

=\(12\left(5^8-1\right)\left(5^8+1\right)\). ... .\(\left(5^{128}+1\right)\)

=\(12\left(5^{64}-1\right)\left(5^{64}+1\right)\left(5^{128}+1\right)\)

=12.\(\left(5^{128}-1\right)\)\(\left(5^{128}+1\right)\)=12.(5²⁵⁶ - 1)

\(\Rightarrow\)A=\(\dfrac{12\left(5^{256}-1\right)}{5^2-1}\)=\(\dfrac{12\left(5^{256}-1\right)}{24}=\dfrac{5^{256}-1}{2}\)<B=5²⁵⁶-1

Vậy A<B.Chúc các bn học tốt