Toán Lớp 9: Phương trình (x+1)² – 3|x+1| + 2 = 0 có bao nhiêu nghiệm?
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Toán Lớp 9: Phương trình (x+1)² – 3|x+1| + 2 = 0 có bao nhiêu nghiệm?
Comments ( 1 )
{\left( {x + 1} \right)^2} – 3\left| {x + 1} \right| + 2 = 0\\
\Leftrightarrow {\left( {\left| {x + 1} \right|} \right)^2} – 3.\left| {x + 1} \right| + 2 = 0\\
Dat:\left| {x + 1} \right| = a\left( {a \ge 0} \right)\\
\Leftrightarrow {a^2} – 3a + 2 = 0\\
\Leftrightarrow {a^2} – a – 2a + 2 = 0\\
\Leftrightarrow \left( {a – 1} \right)\left( {a – 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
a = 1\\
a = 2
\end{array} \right.\left( {tmdk} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
\left| {x + 1} \right| = 1\\
\left| {x + 1} \right| = 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x + 1 = 1\\
x + 1 = – 1\\
x + 1 = 2\\
x + 1 = – 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = – 2\\
x = 1\\
x = – 3
\end{array} \right.\\
Vậy\,x \in \left\{ { – 3; – 2;0;1} \right\}
\end{array}$