Giúp vs thắc mắc quá:|4x-17|=x^2-4x-5.Tìm x nhé 24/11/2021 Bởi Katherine Giúp vs thắc mắc quá:|4x-17|=x^2-4x-5.Tìm x nhé
Đáp án: \(\left[ \begin{array}{l}x = 6\\x = – \sqrt {22} \end{array} \right.\) Giải thích các bước giải: \(\begin{array}{l}\left| {4x – 17} \right| = {x^2} – 4x – 5\\ \to \left[ \begin{array}{l}4x – 17 = {x^2} – 4x – 5\left( {DK:x \ge \dfrac{{17}}{4}} \right)\\ – 4x + 17 = {x^2} – 4x – 5\left( {DK:x < \dfrac{{17}}{4}} \right)\end{array} \right.\\ \to \left[ \begin{array}{l}{x^2} – 8x + 12 = 0\\{x^2} – 22 = 0\end{array} \right.\\ \to \left[ \begin{array}{l}{x^2} – 6x – 2x + 12 = 0\\{x^2} = 22\end{array} \right.\\ \to \left[ \begin{array}{l}x\left( {x – 6} \right) – 2\left( {x – 6} \right) = 0\\x = \sqrt {22} \left( l \right)\\x = – \sqrt {22} \end{array} \right.\\ \to \left[ \begin{array}{l}\left( {x – 2} \right)\left( {x – 6} \right) = 0\\x = – \sqrt {22} \end{array} \right.\\ \to \left[ \begin{array}{l}x = 2\left( l \right)\\x = 6\\x = – \sqrt {22} \end{array} \right.\\ \to \left[ \begin{array}{l}x = 6\\x = – \sqrt {22} \end{array} \right.\end{array}\) Bình luận
Đáp án:
\(\left[ \begin{array}{l}
x = 6\\
x = – \sqrt {22}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left| {4x – 17} \right| = {x^2} – 4x – 5\\
\to \left[ \begin{array}{l}
4x – 17 = {x^2} – 4x – 5\left( {DK:x \ge \dfrac{{17}}{4}} \right)\\
– 4x + 17 = {x^2} – 4x – 5\left( {DK:x < \dfrac{{17}}{4}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^2} – 8x + 12 = 0\\
{x^2} – 22 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^2} – 6x – 2x + 12 = 0\\
{x^2} = 22
\end{array} \right.\\
\to \left[ \begin{array}{l}
x\left( {x – 6} \right) – 2\left( {x – 6} \right) = 0\\
x = \sqrt {22} \left( l \right)\\
x = – \sqrt {22}
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left( {x – 2} \right)\left( {x – 6} \right) = 0\\
x = – \sqrt {22}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 2\left( l \right)\\
x = 6\\
x = – \sqrt {22}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 6\\
x = – \sqrt {22}
\end{array} \right.
\end{array}\)