tìm cặp số x,y thỏa mãn pt x ² + 4√(3-3y) +4y=5x+3x √(y-1)

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tìm cặp số x,y thỏa mãn pt
x ² + 4√(3-3y) +4y=5x+3x √(y-1)

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Cora 1 giờ 2021-09-07T10:23:10+00:00 1 Answers 0 views 0

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    2021-09-07T10:24:12+00:00

    Đáp án: (4;1) hoặc (1;1)

     

    Giải thích các bước giải:

    $\begin{array}{l}
    {x^2} + 4\sqrt {3 – 3y}  + 4y = 5x + 3x\sqrt {y – 1} \\
    DKXD:\,\left\{ \begin{array}{l}
    3 – 3y \ge 0\\
    y – 1 \ge 0
    \end{array} \right. \Rightarrow \left\{ \begin{array}{l}
    y \le 1\\
    y \ge 1
    \end{array} \right. \Rightarrow y = 1\\
    thay\,y = 1\,vao\,pt\,ta\,co:\\
    {x^2} + 4 = 5x\\
     \Rightarrow {x^2} – 5x + 4 = 0\\
     \Rightarrow {x^2} – 4x – x + 4 = 0\\
     \Rightarrow \left( {x – 4} \right)\left( {x – 1} \right) = 0\\
     \Rightarrow \left[ \begin{array}{l}
    x = 4\\
    x = 1
    \end{array} \right.\\
    Vay\,\left( {x;y} \right) = \left( {4;1} \right)hoac\,\left( {1;1} \right)
    \end{array}$

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