Question

1. So sánh 2 số bằng cách vận dụng hằng đẳng thức:

a)A=1999.2001 Vs B=2000²                    b)A=2¹⁶ vs B=(2+1)(2²+1)(2⁴+1)(2⁸+1)

Các bn giải chi tiết nhé!! mk cần gấp!

Answer 1

a, \(A=1999.2001=\left(2000-1\right)\left(2000+1\right)=2000^2-1< 2000^2=B\)

Vậy A<B

b, \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\)

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

Vậy A>B