M = ( √x + 4 )( √x -1 ) / ( √x – 3 )( √x – 2 ) Tìm x để |M| = 3 √x 08/10/2021 Bởi Remi M = ( √x + 4 )( √x -1 ) / ( √x – 3 )( √x – 2 ) Tìm x để |M| = 3 √x
Đáp án: \(\left[ \begin{array}{l}x = 16\\x = \dfrac{{11 + 4\sqrt 7 }}{9}\\x = 0,04914280529\end{array} \right.\) Giải thích các bước giải: \(\begin{array}{l}DK:x \ge 0;x \ne \left\{ {1;4;9} \right\}\\\left| M \right| = 3\sqrt x \\ \to \left[ \begin{array}{l}M = 3\sqrt x \\M = – 3\sqrt x \end{array} \right.\\ \to \left[ \begin{array}{l}\dfrac{{x + 3\sqrt x – 4}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 3\sqrt x \\\dfrac{{x + 3\sqrt x – 4}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = – 3\sqrt x \end{array} \right.\\ \to \left[ \begin{array}{l}\dfrac{{x + 3\sqrt x – 4 – 3\sqrt x \left( {x – 5\sqrt x + 6} \right)}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 0\\\dfrac{{x + 3\sqrt x – 4 + 3\sqrt x \left( {x – 5\sqrt x + 6} \right)}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 0\end{array} \right.\\ \to \left[ \begin{array}{l}x + 3\sqrt x – 4 – 3x\sqrt x + 15x – 18\sqrt x = 0\\x + 3\sqrt x – 4 + 3x\sqrt x – 15x + 18\sqrt x = 0\end{array} \right.\\ \to \left[ \begin{array}{l} – 3x\sqrt x + 16x – 15\sqrt x – 4 = 0\\3x\sqrt x – 14x + 21\sqrt x – 4 = 0\end{array} \right.\\ \to \left[ \begin{array}{l}\left( {4 – \sqrt x } \right)\left( {3x – 4\sqrt x – 1} \right) = 0\\\sqrt x = 0,2216817658\end{array} \right.\\ \to \left[ \begin{array}{l}\sqrt x = 4\\3x – 4\sqrt x – 1 = 0\\\sqrt x = 0,2216817658\end{array} \right.\\ \to \left[ \begin{array}{l}x = 16\\\sqrt x = \dfrac{{2 + \sqrt 7 }}{3}\\\sqrt x = \dfrac{{2 – \sqrt 7 }}{3}\left( l \right)\\x = {\left( {0,2216817658} \right)^2}\end{array} \right.\\ \to \left[ \begin{array}{l}x = 16\\x = {\left( {\dfrac{{2 + \sqrt 7 }}{3}} \right)^2} = \dfrac{{11 + 4\sqrt 7 }}{9}\\x = 0,04914280529\end{array} \right.\end{array}\) Bình luận
Đáp án:
\(\left[ \begin{array}{l}
x = 16\\
x = \dfrac{{11 + 4\sqrt 7 }}{9}\\
x = 0,04914280529
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ge 0;x \ne \left\{ {1;4;9} \right\}\\
\left| M \right| = 3\sqrt x \\
\to \left[ \begin{array}{l}
M = 3\sqrt x \\
M = – 3\sqrt x
\end{array} \right.\\
\to \left[ \begin{array}{l}
\dfrac{{x + 3\sqrt x – 4}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 3\sqrt x \\
\dfrac{{x + 3\sqrt x – 4}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = – 3\sqrt x
\end{array} \right.\\
\to \left[ \begin{array}{l}
\dfrac{{x + 3\sqrt x – 4 – 3\sqrt x \left( {x – 5\sqrt x + 6} \right)}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 0\\
\dfrac{{x + 3\sqrt x – 4 + 3\sqrt x \left( {x – 5\sqrt x + 6} \right)}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x – 2} \right)}} = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x + 3\sqrt x – 4 – 3x\sqrt x + 15x – 18\sqrt x = 0\\
x + 3\sqrt x – 4 + 3x\sqrt x – 15x + 18\sqrt x = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
– 3x\sqrt x + 16x – 15\sqrt x – 4 = 0\\
3x\sqrt x – 14x + 21\sqrt x – 4 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left( {4 – \sqrt x } \right)\left( {3x – 4\sqrt x – 1} \right) = 0\\
\sqrt x = 0,2216817658
\end{array} \right.\\
\to \left[ \begin{array}{l}
\sqrt x = 4\\
3x – 4\sqrt x – 1 = 0\\
\sqrt x = 0,2216817658
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 16\\
\sqrt x = \dfrac{{2 + \sqrt 7 }}{3}\\
\sqrt x = \dfrac{{2 – \sqrt 7 }}{3}\left( l \right)\\
x = {\left( {0,2216817658} \right)^2}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 16\\
x = {\left( {\dfrac{{2 + \sqrt 7 }}{3}} \right)^2} = \dfrac{{11 + 4\sqrt 7 }}{9}\\
x = 0,04914280529
\end{array} \right.
\end{array}\)