Đáp án:
\(\left[ \begin{array}{l}
x = 1,569697569\\
x = 0,4303024308
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK: - 2{x^2} + 4x \ge 0\\
\to - 2x\left( {x - 2} \right) \ge 0\\
\to 0 \le x \le 2\\
{x^2} - 2x + 3 = 2\sqrt { - 2\left( {{x^2} - 2x} \right)} \left( 1 \right)\\
Đặt:\sqrt { - 2\left( {{x^2} - 2x} \right)} = t\left( {t \ge 0} \right)\\
\to - 2\left( {{x^2} - 2x} \right) = {t^2}\\
\to {x^2} - 2x = - \dfrac{{{t^2}}}{2}\\
\left( 1 \right) \to - \dfrac{{{t^2}}}{2} + 3 = 2t\\
\to {t^2} + 4t - 6 = 0\\
\to \left[ \begin{array}{l}
t = - 2 + \sqrt {10} \\
t = - 2 - \sqrt {10} \left( l \right)
\end{array} \right.\\
\to {t^2} = 14 - 4\sqrt {10} \\
\to - 2\left( {{x^2} - 2x} \right) = 14 - 4\sqrt {10} \\
\to {x^2} - 2x = - 7 + 2\sqrt {10} \\
\to \left[ \begin{array}{l}
x = 1,569697569\\
x = 0,4303024308
\end{array} \right.
\end{array}\)
