A=1+2²+2³+2⁴+2⁵+2⁶+2⁷=2+2²+2³+2⁴+2⁵+2⁶+2⁷-1

2A=2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸-2=A-1+2⁸-2

2A-A=2⁸-3

A=256-3=253 không chia hết cho 3

=64

hoặc =256

a/ dkxd:  x # 4; x > 1

\(A=\left(\frac{1}{\sqrt{x}-2}-\frac{2}{x-2\sqrt{x}}\right):\frac{\sqrt{x}-1}{\sqrt{x}}=\left(\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{2}{x-2\sqrt{x}}\right):\frac{\sqrt{x}-1}{\sqrt{x}}\)

\(=\frac{\sqrt{x}-2}{x-2\sqrt{x}}\cdot\frac{\sqrt{x}}{\sqrt{x}-1}=\frac{x-2\sqrt{x}}{\left(x-2\sqrt{x}\right)\left(\sqrt{x}-1\right)}=\frac{1}{\sqrt{x}-1}=\frac{\sqrt{x}+1}{x-1}\)

b/ thay A = 1/2:

 \(A=\frac{\sqrt{x}+1}{x-1}=\frac{1}{2}\Leftrightarrow2\sqrt{x}+2=x-1\Leftrightarrow x=9\)

Ta thấy : \(\left|x-1\right|\ge0\)

\(\left|y+2007\right|\ge0\)

\(\Rightarrow B=\left|x-1\right|=2\left|y+2007\right|-2010\ge-2010\)

\(MaxB=-2010\Leftrightarrow\hept{\begin{cases}x-1=0\\y+2007=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=1\\y=-2007\end{cases}}}\)

giải phóng 2 miền nam bắc