Bài 1:
\(\left(2x-1\right)^2-4x^2\left(2x-3\right)=5\)
\(\Rightarrow4x^2-4x+1-8x^3+12x^2-5=0\)
\(\Rightarrow-8x^3+16x^2-4x-4=0\)
\(\Rightarrow-4\left(2x^3-4x^2+x+1\right)=0\)
\(\Rightarrow2x^3-4x^2+x+1=0\)
\(\Rightarrow2x^3-2x^2-x-2x^2+2x+1=0\)
\(\Rightarrow x\left(2x^2-2x-1\right)-\left(2x^2-2x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(2x^2-2x-1\right)=0\)
\(\Rightarrow\left[\begin{matrix}x-1=0\\2x^2-2x-1=0\end{matrix}\right.\)\(\Rightarrow\left[\begin{matrix}x=1\\\Delta_{2x^2-2x-1}=\left(-2\right)^2-\left(-4\left(2.1\right)\right)=12\end{matrix}\right.\)
\(\Rightarrow\left[\begin{matrix}x=1\\x_{1,2}=\frac{2\pm\sqrt{12}}{4}\end{matrix}\right.\)
Bài 2:
a)\(x^2+6x-y^2+9\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
b)\(2x^2-3xy-2y^2+5x+5y-3\)
\(=2x^2+xy-x-4xy-2y^2+2y+6x+3y-3\)
\(=x\left(2x+y-1\right)-2y\left(2x+y-1\right)+3\left(2x+y-1\right)\)
\(=\left(x-2y+3\right)\left(2x+y-1\right)\)
