a)
\(\left(1-2x\right)\cdot\left(1+2x\right)+\left(2x+3\right)^2=34\\ \Leftrightarrow1-4x^2+4x^2+12x+9=34\\ \Leftrightarrow12x+10=34\\ \Rightarrow x=\frac{34-10}{12}=2\)
b)
\(\left(2x-3\right)^2+\left(3-2x\right)\cdot\left(x-1\right)=0\\ \Leftrightarrow4x^2-12x+9+3x-3-2x^2+2x=0\\ \Leftrightarrow2x^2-7x+6=0\\ \Leftrightarrow6-7x+2x^2=0\\ \Leftrightarrow6-3x-4x+2x^2=0\\ \Leftrightarrow3\cdot\left(2-x\right)-2x\cdot\left(2-x\right)=0\\ \Leftrightarrow\left(3-2x\right)\cdot\left(2-x\right)=0\\\Rightarrow\left[{}\begin{matrix}3-2x=0\\2-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\frac{3}{2}\\x=2\end{matrix}\right.\)
\(a,\left(1-2x\right)\left(1+2x\right)+\left(2x+3\right)^2=34\)
\(1-4x^2+4x^2+12x+9=34\)
\(10+12x=34\)
\(12x=24\)
\(x=2\)
\(b,\left(2x-3\right)^2+\left(3-2x\right)\left(x-1\right)=0\)
\(4x^2+12x+9+3x-3-2x^2+2x=0\)
\(2x^2-7x+6=0\)
\(2x^2-3x-4x+6=0\)
\(x\left(2x-3\right)-2\left(2x-3\right)=0\)
\(\left(x-2\right)\left(2x-3\right)=0\)
\(\left[{}\begin{matrix}x-2=0\\2x-3=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=2\\x=\frac{3}{2}\end{matrix}\right.\)
\(\left(1-2x\right)\left(1+2x\right)+\left(2x+3\right)^2=34\)
\(1-4x^2+4x^2+12x+9=34\)
\(12x+10=34\)
\(12x=24\Rightarrow x=2\)
b)\(\left(2x-3\right)^2+\left(3-2x\right)\left(x-1\right)=0\)
\(4x^2-12x+9+3x-3-2x^2_{ }+2x=0\)
\(2x^2-7x+6=0\)
\(\left(x-2\right)\left(2x-3\right)=0\)
\(\left[{}\begin{matrix}x-2=0\\2x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{3}{2}\end{matrix}\right.\)