a) Ta có: \(x^2-25=0\)
\(\Leftrightarrow x^2=25\)
hay \(x\in\left\{5;-5\right\}\)
Vậy: \(x\in\left\{5;-5\right\}\)
b) Ta có: \(\left(x-4\right)^2-36=0\)
\(\Leftrightarrow\left(x-4\right)^2=36\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=6\\x-4=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)
Vậy: \(x\in\left\{10;-2\right\}\)
c) Ta có: \(\left(6-x\right)^2=0\)
\(\Leftrightarrow6-x=0\)
hay x=6
Vậy: x=6
d) Ta có: \(\left(x+\frac{1}{4}\right)^2-\frac{1}{9}=0\)
\(\Leftrightarrow\left(x+\frac{1}{4}\right)^2=\frac{1}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{1}{4}=\frac{1}{3}\\x+\frac{1}{4}=\frac{-1}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{12}\\x=\frac{-7}{12}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{1}{12};\frac{-7}{12}\right\}\)