Question

x² -4x+3>0

x³ -2x² +3x-2>=0

Answer 1

a) x²-3x-x+3>0

<=> x(x-3)-(x-3)>0

<=> (x-3)(x-1)>0

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3>0\\x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3< 0\\x-1< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>3\\x>1\end{matrix}\right.\\\left\{{}\begin{matrix}x< 3\\x< 1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>3\\x< 1\end{matrix}\right.\)

Answer 2

b) x³-2x²+3x-2\(\ge\) 0

<=> x³-x²-x²+x+2x-2\(\ge0\)

<=> (x-1)(x²-x+2)\(\ge0\)

Vì x²-x+2\(\ge0\)

nên x-1\(\ge0\)

x>=1