Question

x³ + 2x² − 13x + 10 = 0

Answer 1

\(\Leftrightarrow x^3-2x^2+4x^2-8x-5x+10=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^2+4x-5\right)=0\)

=>(x-2)(x+5)(x-1)=0

hay \(x\in\left\{2;-5;1\right\}\)

Answer 2

\(x^3+2x^2-13x+10=0\)

\(\left(x^3-x^2\right)+\left(3x^2-3x\right)-\left(10x-10\right)=0\)

\(x^2\left(x-1\right)+3x\left(x-1\right)-10\left(x-1\right)=0\)

\(\left(x-1\right)\left(x^2+3x-10\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2+3x=10\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\\left(x+\dfrac{3}{2}\right)^2=\dfrac{49}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-5\end{matrix}\right.\)