c. \(3x^2-7x-10=0\)
\(\Leftrightarrow\left(x-\dfrac{10}{3}\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{10}{3}=0\\x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{10}{3}\\x=-1\end{matrix}\right.\)
b. \(2x\left(x-10\right)-x+10=0\)
\(\Leftrightarrow2x\left(x-10\right)-\left(x-10\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-10=0\\2x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=\dfrac{1}{2}\end{matrix}\right.\)
c. \(3x^3+7x^2+17x+5=0\)
\(\Leftrightarrow x^2\left(3x+1\right)+2x\left(3x+1\right)+5\left(3x+1\right)=0\)
\(\Leftrightarrow\left(3x+1\right)\left(x^2+2x+5\right)=0\)
mà \(x^2+2x+5=\left(x+1\right)^2+4\ge4>0\forall x\)
\(\Leftrightarrow3x+1=0\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
f. \(\left(2x-1\right)^2-\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(2x-1-x+3\right)\left(2x-1+x-3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\3x-4=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{4}{3}\end{matrix}\right.\)
g. \(x^3-5x^2+8x=4\)
\(\Leftrightarrow x^3-5x^2+8x-4=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)