tim cac so nguyen duong thoa man x^2-y^2=105 bn nào lm đug mk cho 5***** lun .mong các bn giúp

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1. Đáp án:

   \[\left( {x;y} \right) = \left\{ {\left( {53;52} \right);\left( {19;16} \right);\left( {13;8} \right);\left( {11;4} \right)} \right\}\]

   Giải thích các bước giải:

    Ta có:

   \(\begin{array}{l}
   {x^2} – {y^2} = 105\\
    \Leftrightarrow \left( {x – y} \right)\left( {x + y} \right) = 105\\
   x,y \in {Z^ + } \Rightarrow \left\{ \begin{array}{l}
   \left( {x + y} \right) \in {Z^ + }\\
   x + y \ge 2\\
   x + y > x – y
   \end{array} \right.\\
   105 = 1.105 = 3.35 = 5.21 = 7.15\\
    \Rightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x + y = 105\\
   x – y = 1
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x + y = 35\\
   x – y = 3
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x + y = 21\\
   x – y = 5
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x + y = 15\\
   x – y = 7
   \end{array} \right.
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x = 53\\
   y = 52
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x = 19\\
   y = 16
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x = 13\\
   y = 8
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x = 11\\
   y = 4
   \end{array} \right.
   \end{array} \right.\\
    \Rightarrow \left( {x;y} \right) = \left\{ {\left( {53;52} \right);\left( {19;16} \right);\left( {13;8} \right);\left( {11;4} \right)} \right\}
   \end{array}\)

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