chào Doramon hoidap247

\(4x^2+4x+1=x^2\)

\(\Leftrightarrow\left[\left(2x\right)^2+2.2x.1+1^2\right]-x^2=0\)

\(\Leftrightarrow\left(2x+1\right)^2-x^2=0\)

\(\Leftrightarrow\left(2x+1-x\right).\left(2x+1+x\right)=0\)

\(\Leftrightarrow\left(x+1\right).\left(3x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\3x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy nghiệm của phương trình là: \(S=\left\{-1;-\dfrac{1}{3}\right\}\)

\(\left(x^2-9\right)^2-9.\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right).\left(x+3\right).\left(x-3\right).\left(x+3\right)-9.\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right)^2.\left[\left(x+3\right)^2-9\right]=0\)

\(\Leftrightarrow\left(x-3\right)^2.\left[\left(x+3-3\right).\left(x+3+3\right)\right]=0\)

\(\Leftrightarrow\left(x-3\right)^2.x.\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-3\right)^2=0\\x=0\\x+6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\\x=-6\end{matrix}\right.\)

Vậy nghiệm của phương trình là: \(S=\left\{0;3;-6\right\}\)

\(\dfrac{2x-5}{x+5}=3\) (x \(\ne\)-5)

\(\Leftrightarrow\dfrac{2x-5}{x+5}=\dfrac{3.\left(x+5\right)}{x+5}\)

\(\Leftrightarrow2x-5=3x+15\)

\(\Leftrightarrow2x-3x=15+5\)

\(\Leftrightarrow x=-20\left(tm\right)\)

Vậy nghiệm của phương là: \(S=\left\{-20\right\}\)