Toán căn(x+2cănx-1) = 2 giải hộ với, cần gấp ạ 08/09/2021 By Aubrey căn(x+2cănx-1) = 2 giải hộ với, cần gấp ạ
\(\begin{array}{l} \sqrt {x + 2\sqrt x – 1} = 2\,\,\left( {x \ge 0} \right)\\ \Rightarrow x + 2\sqrt x – 1 = 4\\ \Leftrightarrow 2\sqrt x = 5 – x\,\,\left( {x \le 5} \right)\\ \Leftrightarrow 4x = 25 – 10x + {x^2}\\ \Leftrightarrow {x^2} – 14x + 25 = 0\\ \Leftrightarrow {\left( {x – 7} \right)^2} – 24 = 0\\ \Leftrightarrow {\left( {x – 7} \right)^2} = 24\\ \Leftrightarrow \left[ \begin{array}{l} x = 7 + 2\sqrt 6 \left( {ktm} \right)\\ x = 7 – 2\sqrt 6 \left( {tm} \right) \end{array} \right. \end{array}\) Trả lời
\(\begin{array}{l}
\sqrt {x + 2\sqrt x – 1} = 2\,\,\left( {x \ge 0} \right)\\
\Rightarrow x + 2\sqrt x – 1 = 4\\
\Leftrightarrow 2\sqrt x = 5 – x\,\,\left( {x \le 5} \right)\\
\Leftrightarrow 4x = 25 – 10x + {x^2}\\
\Leftrightarrow {x^2} – 14x + 25 = 0\\
\Leftrightarrow {\left( {x – 7} \right)^2} – 24 = 0\\
\Leftrightarrow {\left( {x – 7} \right)^2} = 24\\
\Leftrightarrow \left[ \begin{array}{l}
x = 7 + 2\sqrt 6 \left( {ktm} \right)\\
x = 7 – 2\sqrt 6 \left( {tm} \right)
\end{array} \right.
\end{array}\)