Bài tập 4.26 trang 108 SBT Toán 10

a) \(\left( {x + 1} \right)\left( {2x - 1} \right) + x \le 3 + 2{x^2}\)

\(\begin{array}{l}
 \Leftrightarrow 2{x^2} + 2x - 1 \le 3 + 2{x^2}\\
 \Leftrightarrow 2x \le 4 \Leftrightarrow x \le 2
\end{array}\)

b) \(\left( {x + 1} \right)\left( {x + 2} \right)\left( {x + 3} \right) - x > {x^3} + 6{x^2} - 5\)

\(\begin{array}{l}
 \Leftrightarrow {x^3} + 6{x^2} + 10x + 6 > {x^3} + 6{x^2} - 5\\
 \Leftrightarrow 10x >  - 11 \Leftrightarrow x >  - \frac{{11}}{{10}}
\end{array}\)

c) \(x + \sqrt x  > \left( {2\sqrt x  + 3} \right)\left( {\sqrt x  - 1} \right)\)

\(\begin{array}{l}
 \Leftrightarrow \left\{ \begin{array}{l}
x \ge 0\\
x + \sqrt x  > 2x + \sqrt x  - 3
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x \ge 0\\
3 > x
\end{array} \right. \Leftrightarrow 0 \le x < 3
\end{array}\)

-- Mod Toán 10 HỌC247