Question

1. Tính hoặc rút gọn
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)+1\)

Answer 1

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

Đặt x = \(2^2+1\)ta được :

\(3x.x^2.x^4.x^8\)+1

= \(3x^{15}\)+1

thay x=\(2^2+1\)ta được:

\(3\left(2^2+1\right)^{15}+1=3.5^{15}+1\)

 

Answer 2

3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)+1

=3x5x17x257x65537+1

=4294967296

chọn đúng cho mình điểm nha!

Answer 3

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

\(=3\left(4+1\right)\left(16+1\right)\left(256+1\right)\left(65536+1\right)+1\)

\(=3\cdot5\cdot17\cdot257\cdot65537+1\)

\(=4294967295+1\)

\(=4294967296\)