1)
\(\left(2x+7\right)^2=9\left(x+2\right)^2\\ \Leftrightarrow\left(2x+7\right)^2=\left(3x+6\right)^2\\ \Leftrightarrow\left(2x+7\right)^2-\left(3x+6\right)^2=0\\ \Leftrightarrow\left(2x+7+3x+6\right)\left(2x+7-3x-6\right)=0\\ \Leftrightarrow\left(5x+13\right)\left(1-x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}5x=-13\\x=1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{13}{5}\\x=1\end{matrix}\right.\)
Vậy: ...
2)
\(\left(x+2\right)=9\left(x^2+4x+4\right)\\ \Leftrightarrow\left(x+2\right)=9\left(x+2\right)^2\\ \Leftrightarrow9\left(x+2\right)^2-\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left[9\left(x+2\right)-1\right]=0\\ \Leftrightarrow\left(x+2\right)\left(9x+17\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\9x=-17\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-\dfrac{17}{9}\end{matrix}\right.\)
Vậy: ...
3)
\(4\left(2x+7\right)^2-9\left(x+3\right)^2=0\\ \Leftrightarrow\left(4x+14\right)^2-\left(3x+9\right)^2=0\\ \Leftrightarrow\left(4x+14+3x+9\right)\left(4x+14-3x-9\right)=0\\ \Leftrightarrow\left(7x+23\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}7x=-23\\x=5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-23}{7}\\x=5\end{matrix}\right.\)
Vậy: ...
4)
\(\left(5x^2-2x+10\right)^2=\left(3x^2+10x-8\right)^2\\ \Leftrightarrow\left(5x^2-2x+10\right)^2-\left(3x^2+10x-8\right)^2=0\\\Leftrightarrow\left(5x^2-2x+10+3x^2+10x-8\right)\left(5x^2-2x+10-3x^2-10x+8\right)=0\\ \Leftrightarrow\left(8x^2+8x+2\right)\left(2x^2-12x+18\right)=0\\ \Leftrightarrow4\left(4x^2+4x+1\right)\left(x^2-6x+9\right)\\ \Leftrightarrow4\left(2x+1\right)^2\left(x-3\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}4x=-1\\x=3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=3\end{matrix}\right.\)
Vậy: ...
