\(x-2\sqrt{x}=0\)

\(\sqrt{x}.\left(\sqrt{x}-2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\sqrt{x}=0\\\sqrt{x}-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\\sqrt{x}=2\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)

                   vay \(\orbr{\begin{cases}x=0\\x=4\end{cases}}\)

1) 5x - \(\frac{2}{3}\)= \(\frac{-3}{2}\)+ 1 

5x + \(\frac{3}{2}x\)= 1 + \(\frac{2}{3}\)

\(\frac{13}{2}x\)= \(\frac{5}{3}\)

x = \(\frac{5}{3}.\frac{2}{13}\)

x = \(\frac{10}{39}\)

2) -7x + \(\frac{7}{3}\)= \(\frac{3}{5}x+\frac{4}{9}\)

-7x - \(\frac{-3}{5}x\)= \(\frac{4}{9}-\frac{7}{3}\)

\(\frac{-38}{5}x=\frac{-17}{9}\)

x = \(\frac{-17}{9}.\frac{-5}{38}\)

x = \(\frac{85}{342}\)

3) \(\frac{4}{5}x-\frac{1}{3}=2x-\frac{3}{4}\)

\(\frac{4}{5}x-2x=\frac{-3}{4}+\frac{1}{3}\)

\(\frac{-6}{5}x=\frac{-5}{12}\)

\(x=\frac{-5}{12}.\frac{-5}{6}\)

x = \(\frac{25}{72}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{x}{3}=\frac{y}{4}=\frac{z}{6}=\frac{x+2y-z}{3+2.4-6}=\frac{-20}{5}=-4\)

\(\frac{x}{3}=-4\Leftrightarrow x=-12\)

\(\frac{2y}{4}=-4\Leftrightarrow2y=-16\Rightarrow y=-8\)

\(\frac{z}{6}=-4\Leftrightarrow z=-24\)

Vậy x=-12 ; y=-8 và z=-24

\(\frac{x}{3}=\frac{y}{4}=\frac{z}{6}\Rightarrow\frac{x}{3}=\frac{2y}{8}=\frac{z}{6}\)

theo tính chất của tỉ lệ thức

\(\frac{x-2y+z}{3-8+6}=\frac{-20}{1}=-20\) rồi có \(\frac{x}{3}=-20,\frac{y}{4}=-20,\frac{z}{6}=-20\),\(\Rightarrow x=\frac{20}{3},y=5,z=\frac{10}{3}\)

M = 2²⁰¹⁰ - ( 2²⁰⁰⁹ + 2²⁰⁰⁸ + 2²⁰⁰⁷ + ... + 2¹ + 2⁰ )

2M=\(2^{2011}-2^{2010}-....-2^2-2\)

2M-M=\(2^{2011}-2^{2010}-2^{2010}-1\)

M=\(2^{2011}-2.2^{2010}-1\)

M=1