M.n giúp mik vs mik đag cần gấp ạ cảm ơn mấy bẹn dễ thương nhiều October 16, 2020 by Ladonna M.n giúp mik vs mik đag cần gấp ạ cảm ơn mấy bẹn dễ thương nhiều
Đáp án: $\begin{array}{l}Dkxd:x \ge 1;y \ge 2;z \ge 3\\x + y + z + 8 = 2\sqrt {x – 1} + 4\sqrt {y – 2} + 6\sqrt {z – 3} \\ \Rightarrow x – 1 – 2\sqrt {x – 1} + 1\\ + y – 2 – 4\sqrt {y – 2} + 4\\ + z – 3 – 6\sqrt {z – 3} + 9 = 0\\ \Rightarrow {\left( {\sqrt {x – 1} – 1} \right)^2} + {\left( {\sqrt {y – 2} – 2} \right)^2} + {\left( {\sqrt {z – 3} – 3} \right)^2} = 0\\ \Rightarrow \left\{ \begin{array}{l}\sqrt {x – 1} = 1\\\sqrt {y – 2} = 2\\\sqrt {z – 3} = 3\end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l}x – 1 = 1\\y – 2 = 4\\z – 3 = 9\end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l}x = 2\\y = 6\\z = 12\end{array} \right.\left( {tmdk} \right)\\Vay\,\left( {x;y;z} \right) = \left( {2;6;12} \right)\end{array}$ Reply
Đáp án:
$\begin{array}{l}
Dkxd:x \ge 1;y \ge 2;z \ge 3\\
x + y + z + 8 = 2\sqrt {x – 1} + 4\sqrt {y – 2} + 6\sqrt {z – 3} \\
\Rightarrow x – 1 – 2\sqrt {x – 1} + 1\\
+ y – 2 – 4\sqrt {y – 2} + 4\\
+ z – 3 – 6\sqrt {z – 3} + 9 = 0\\
\Rightarrow {\left( {\sqrt {x – 1} – 1} \right)^2} + {\left( {\sqrt {y – 2} – 2} \right)^2} + {\left( {\sqrt {z – 3} – 3} \right)^2} = 0\\
\Rightarrow \left\{ \begin{array}{l}
\sqrt {x – 1} = 1\\
\sqrt {y – 2} = 2\\
\sqrt {z – 3} = 3
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x – 1 = 1\\
y – 2 = 4\\
z – 3 = 9
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 2\\
y = 6\\
z = 12
\end{array} \right.\left( {tmdk} \right)\\
Vay\,\left( {x;y;z} \right) = \left( {2;6;12} \right)
\end{array}$