a) Ta có: \(2-25x^2=0\)
\(\Leftrightarrow25x^2=2\)
\(\Leftrightarrow x^2=\frac{2}{25}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{2}}{5}\\x=-\frac{\sqrt{2}}{5}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{\sqrt{2}}{5};-\frac{\sqrt{2}}{5}\right\}\)
b) Ta có: \(x^2-x+\frac{1}{4}=0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\frac{1}{2}+\left(\frac{1}{2}\right)^2=0\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=0\)
\(\Leftrightarrow x-\frac{1}{2}=0\)
hay \(x=\frac{1}{2}\)
Vậy: \(x=\frac{1}{2}\)
c) Ta có: \(x\left(x-2\right)+x-2=0\)
\(\Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
Vậy: \(x\in\left\{-1;2\right\}\)
d) Ta có: \(5x\left(x-3\right)-x+3=0\)
\(\Leftrightarrow5x\left(x-3\right)-\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\5x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\5x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\frac{1}{5}\end{matrix}\right.\)
Vậy: \(x\in\left\{3;\frac{1}{5}\right\}\)
e) Ta có: \(x^3-\frac{1}{4}x=0\)
\(\Leftrightarrow x\left(x^2-\frac{1}{4}\right)=0\)
\(\Leftrightarrow x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-\frac{1}{2}=0\\x+\frac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{0;\frac{1}{2};-\frac{1}{2}\right\}\)
g) Ta có: \(\left(2x-1\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\3x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\frac{2}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{4;-\frac{2}{3}\right\}\)
