a) \(A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=.............................................................\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1=B-1\)

Suy ra A < B

b) \(A=2015.2017=\left(2016-1\right)\left(2016+1\right)=2016^2-1=B-1\)

Suy ra A < B

Phần a bạn nhân thêm ở A là (2-1) là ra hằng đẳng thức, cứ thế mà triển. (Kết quả: A<B)

Phần b: phân tích A, ta có:

2015.2017= (2016-1).(2016+1)= 2016^2 -1 <2016^2

Suy ra: A<B

TÌM TRƯỚC KHI HỎI

a)Ta có: \(2015=2016-1;2017=2016+1\)

\(\Rightarrow A=2015\cdot2017=\left(2016-1\right)\left(2016+1\right)=2016^2-1< 2016^2=B\)

b)Ta có:

\(C=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

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

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1< 2^{32}=D\)

a)Ta có:A=2015.2017=(2016-1)(2016+1)=2016²-1<B=2016²

b)Ta có:C=(2+1)(22+1)(24+1)(28+1)(216+1)

=(2-1)(2+1)(22+1)(24+1)(28+1)(216+1)=(2²-1)(22+1)(24+1)(28+1)(216+1)

=(2⁴-1)(24+1)(28+1)(216+1)=(2⁸-1)(28+1)(216+1)=(2¹⁶-1)(216+1)=2³²-1

=>C<D=2³²

\(a,B=2016^2=\left(2017-1\right)^2=2017^2-2.2017+1=2017.\left(2017-2\right)+1=2017.2015+1>2017.2015\)Hay A<B

Ax(2-1)=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)=(2^4-1)(2^4+1)(2^8+1)(2^16+1)=(2^8-1)(2^8+1)(2^16+1)=(2^16-1)(2^16+1)=2^32-1

Vậy A=B

Áp dụng hằng đẵng thức A^2-B^2 đó bạn

what the fuck

Có

a) A= 2015. 2017 = ( 2016 - 1)(2016 + 1)
= 2016² - 1 < 2016² = B
=> A < B ( 2016² - 1 < 2016² )

b) C = (2+1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)
= ( 2 - 1)(2+1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)
= (2² - 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)
= ( 2⁴ - 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)
= (2⁸ -1)(2⁸ + 1)(2¹⁶ + 1)
= ( 2¹⁶ - 1)( 2¹⁶ + 1)
= 2³² - 1 > 2²³ = D
Vậy C > D ( 2³² - 1 < 2²³ )

Ta có: \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

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

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

\(=2^{32}-1< 2^{32}\)

\(\Leftrightarrow A< B\)

a)\(A=26^2-24^2=\left(26-24\right)\left(26+24\right)=2.50\)

\(B=27^2-25^2=\left(27-25\right)\left(27+25\right)=2.52\)

Vì 52 > 50 nên B > A