\(1.\left(2x+7\right)^2=\left(x+3\right)^2\\ \Leftrightarrow\left(2x+7\right)^2-\left(x+3\right)^2=0\\ \left(2x+7-x-3\right)\left(2x+7+x+3\right)=0\\ \Leftrightarrow\left(x+4\right)\left(3x+10\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{10}{3}\end{matrix}\right.\\ 2.\left(4x+14\right)^2=\left(7x+21\right)^2\\ \Leftrightarrow\left(4x+14\right)^2-\left(7x+21\right)^2=0\\ \Leftrightarrow\left(4x+14-7x-21\right)\left(4x+14+7x+21\right)=0\\ \Leftrightarrow\left(-3x-7\right)\left(11x+35\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{3}\\x=-\dfrac{35}{11}\end{matrix}\right.\\ 3.\left(13x-7\right)^2=\left(7x+9\right)^2\\ \Leftrightarrow\left(13x-7\right)^2-\left(7x+9\right)^2=0\\ \Leftrightarrow\left(13x-7-7x-9\right)\left(13x-7+7x+9\right)=0\\ \Leftrightarrow\left(6x-16\right)\left(19x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{16}{6}=\dfrac{8}{3}\\x=-\dfrac{2}{19}\end{matrix}\right.\)
1: \(\left(2x+7\right)^2=\left(x+3\right)^2\)
=>\(\left(2x+7\right)^2-\left(x+3\right)^2=0\)
=>(2x+7-x-3)(2x+7+x+3)=0
=>(x+4)(3x+10)=0
=>\(\left[{}\begin{matrix}x+4=0\\3x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{10}{3}\end{matrix}\right.\)
2: \(\left(4x+14\right)^2=\left(7x+21\right)^2\)
=>\(\left(7x+21\right)^2-\left(4x+14\right)^2=0\)
=>(7x+21-4x-14)(7x+21+4x+14)=0
=>(3x+7)(11x+35)=0
=>\(\left[{}\begin{matrix}3x+7=0\\11x+35=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{3}\\x=-\dfrac{35}{11}\end{matrix}\right.\)
3: \(\left(13x-7\right)^2=\left(7x+9\right)^2\)
=>\(\left(13x-7\right)^2-\left(7x+9\right)^2=0\)
=>(13x-7-7x-9)(13x-7+7x+9)=0
=>(6x-16)(20x+2)=0
=>(3x-8)(10x+1)=0
=>\(\left[{}\begin{matrix}3x-8=0\\10x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=-\dfrac{1}{10}\end{matrix}\right.\)
4: \(\left(6-9x\right)^2=\left(5x-7\right)^2\)
=>\(\left(9x-6\right)^2-\left(5x-7\right)^2=0\)
=>(9x-6-5x+7)(9x-6+5x-7)=0
=>(4x+1)(14x-13)=0
=>\(\left[{}\begin{matrix}4x+1=0\\14x-13=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=\dfrac{13}{14}\end{matrix}\right.\)
5: \(\left(27x+9\right)^2=\left(24x-7\right)^2\)
=>\(\left(27x+9\right)^2-\left(24x-7\right)^2=0\)
=>(27x+9-24x+7)(27x+9+24x-7)=0
=>(3x+16)(51x+2)=0
=>\(\left[{}\begin{matrix}3x+16=0\\51x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{16}{3}\\x=-\dfrac{2}{51}\end{matrix}\right.\)
6: \(\left(-5x-1\right)^2=\left(x-2\right)^2\)
=>\(\left(5x+1\right)^2=\left(x-2\right)^2\)
=>(5x+1-x+2)(5x+1+x-2)=0
=>(4x+3)(6x-1)=0
=>\(\left[{}\begin{matrix}4x+3=0\\6x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=\dfrac{1}{6}\end{matrix}\right.\)
7: \(\left(3-x\right)^2=\left(x+3\right)^2\)
=>\(x^2-6x+9=x^2+6x+9\)
=>-6x=6x
=>x=0
8: \(\left(4x-6\right)^2=\left(4x+6\right)^2\)
=>\(\left(4x-6\right)^2-\left(4x+6\right)^2=0\)
=>(4x-6-4x-6)(4x-6+4x+6)=0
=>-12*8x=0
=>-96x=0
=>x=0
9: \(\left(1+x\right)^2=\left(x-1\right)^2\)
=>\(x^2+2x+1=x^2-2x+1\)
=>2x=-2x
=>4x=0
=>x=0
10: \(\left(2x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{2}-2x\right)^2\)
=>\(\left(2x+\dfrac{1}{2}-\dfrac{1}{2}+2x\right)\left(2x+\dfrac{1}{2}+\dfrac{1}{2}-2x\right)=0\)
=>4x=0
=>x=0
11: \(\left(5x-4\right)^2=\left(4-5x\right)^2\)
=>\(25x^2-40x+16=16-40x+25x^2\)
=>0x=0(luôn đúng)
