Question

So sánh 

A=3^32-1

B=(3+1).(3^2+1).(3^4+1).(3^8+1).(3^16 +1).2

Answer 1

B=(3+1).(3^2+1).(3^4+1).(3^8+1).(3^16 +1).2

=>B=2.(3+1)(3²+1)(3⁴+1)(3⁸+1).(3¹⁶+1)

=(3-1)(3+1)(3²+1)(3⁴+1)(3⁸+1).(3¹⁶+1)

=(3²-1)(3²+1)(3⁴+1)(3⁸+1).(3¹⁶+1)

=(3⁴-1)(3⁴+1)(3⁸+1).(3¹⁶+1)

=(3⁸-1)(3⁸+1).(3¹⁶+1)

=(3¹⁶-1)(3¹⁶+1)

=3³²-1=A

Vậy A=B

Answer 2

\(B=2.\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right).\left(3^{16}+1\right)\)

    \(=\left(3-1\right).\left(3+1\right).\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)

     \(=\left(3^2-1\right).\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)

     \(=\left(3^4-1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)

     \(=\left(3^8-1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)

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

     \(=3^{32}-1\)

Vậy A = B = 3³² - 1

Answer 3

ta có A=3³²-1=(3¹⁶+1)(3¹⁶-1)=(3¹⁶+1)(3⁸+1)(3⁸-1)=(3¹⁶+1)(3⁸+1)(3⁴+1)(3⁴-1)

=(3¹⁶+1)(3⁸+1)(3⁴+1)(3²+1)(3²-1)=(3¹⁶+1)(3⁸+1)(3⁴+1)(3²+1)(3+1)(3-1)=B

=> A=B