Rất gấp Vote 5 sao |x+2|+|x-3|=5 |3x-2|+|2x-1|=3 |1-3x|+|2x+5|=9

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1. Đáp án:

   c. \(\left[ \begin{array}{l}
   x = 15\\
   x =  – 3
   \end{array} \right.\)

   Giải thích các bước giải:

   \(\begin{array}{l}
   a.\left| {x + 2} \right| + \left| {x – 3} \right| = 5\\
    \to {\left( {x + 2} \right)^2} + 2\left( {x + 2} \right)\left( {x – 3} \right) + {\left( {x – 3} \right)^2} = 25\\
    \to {x^2} + 4x + 4 + 2\left( {{x^2} – x – 6} \right) + {x^2} – 6x + 9 = 25\\
    \to 4{x^2} – 4x – 24 = 0\\
    \to {x^2} – x – 6 = 0\\
    \to \left( {x + 2} \right)\left( {x – 3} \right) = 0\\
    \to \left[ \begin{array}{l}
   x + 2 = 0\\
   x – 3 = 0
   \end{array} \right.\\
    \to \left[ \begin{array}{l}
   x =  – 2\\
   x = 3
   \end{array} \right.\\
   b.\left| {3x – 2} \right| + \left| {2x – 1} \right| = 3\\
    \to {\left( {3x – 2} \right)^2} + 2\left( {3x – 2} \right)\left( {2x – 1} \right) + {\left( {2x – 1} \right)^2} = 9\\
    \to 9{x^2} – 12x + 4 + 2\left( {6{x^2} – 7x + 2} \right) + 4{x^2} – 4x + 1 = 9\\
    \to 25{x^2} – 30x = 0\\
    \to 5x\left( {5x – 6} \right) = 0\\
    \to \left[ \begin{array}{l}
   x = 0\\
   5x – 6 = 0
   \end{array} \right.\\
    \to \left[ \begin{array}{l}
   x = 0\\
   x = \frac{6}{5}
   \end{array} \right.\\
   c.\left| {1 – 3x} \right| + \left| {2x + 5} \right| = 9\\
    \to {\left( {1 – 3x} \right)^2} + 2\left( {1 – 3x} \right)\left( {2x + 5} \right) + {\left( {2x + 5} \right)^2} = 81\\
    \to 1 – 6x + 9{x^2} + 2\left( { – 6{x^2} – 13x + 5} \right) + 4{x^2} + 20x + 25 = 81\\
    \to {x^2} – 12x – 45 – 0\\
    \to {x^2} – 15x + 3x – 45 = 0\\
    \to x\left( {x – 15} \right) + 3\left( {x – 15} \right) = 0\\
    \to \left[ \begin{array}{l}
   x – 15 = 0\\
   x + 3 = 0
   \end{array} \right.\\
    \to \left[ \begin{array}{l}
   x = 15\\
   x =  – 3
   \end{array} \right.
   \end{array}\)

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