Question

[Nguyễn Hoài Phương]

(x-2)^6=4+2^2+2^3+2^4+.....+2^2021

Answer 1

[Nguyễn Lê Phước Thịnh]

Đặt \(A=2^2+2^3+...+2^{2021}\)

=>\(2A=2^3+2^4+...+2^{2022}\)

=>\(2A-A=2^3+2^4+...+2^{2022}-2^2-2^3-...-2^{2021}\)

=>\(A=2^{2022}-4\)

\(\left(x-2\right)^6=4+2^2+2^3+...+2^{2021}\)

=>\(\left(x-2\right)^6=4+2^{2022}-4=2^{2022}\)

=>\(\left(x-2\right)^6=\left(2^{337}\right)^6\)

=>\(\left[{}\begin{matrix}x-2=2^{337}\\x-2=-2^{337}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2+2^{337}\\x=-2^{337}+2\end{matrix}\right.\)