Question

mik cần gấp

 

Answer 1

Sửa đề: \(\left(x-2021\right)^2-1=1+2+\cdots+2^{99}\)

Đặt \(A=1+2+2^2+\cdots+2^{99}\)

=>\(2A=2+2^2+\cdots+2^{100}\)

=>\(2A-A=2+2^2+\cdots+2^{100}-1-2-\cdots-2^{99}\)

=>\(A=2^{100}-1\)

Ta có: \(\left(x-2021\right)^2-1=1+2+\cdots+2^{99}\)

=>\(\left(x-2021\right)^2-1=2^{100}-1\)

=>\(\left(x-2021\right)^2=2^{100}=\left(2^{50}\right)^2\)

=>\(\left[\begin{array}{l}x-2021=2^{50}\\ x-2021=-2^{50}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2^{50}+2021\\ x=-2^{50}+2021\end{array}\right.\)