Đáp án:
\(\left[ \begin{array}{l}
x = 1\\
x = 8,502201405
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
{x^2} - 6x + 9 = 4\sqrt {{x^2} - 2x + 2} \\
\to {x^4} + 36{x^2} + 81 - 12{x^3} + 18{x^2} - 108x = 16\left( {{x^2} - 2x + 2} \right)\\
\to {x^4} - 12{x^3} + 38{x^2} - 76x + 49 = 0\\
\to {x^4} - {x^3} - 11{x^3} + 11{x^2} + 27{x^2} - 27x - 49x + 49 = 0\\
\to {x^3}\left( {x - 1} \right) - 11{x^2}\left( {x - 1} \right) + 27x\left( {x - 1} \right) - 49\left( {x - 1} \right) = 0\\
\to \left( {x - 1} \right)\left( {{x^3} - 11{x^2} + 27x - 49} \right) = 0\\
\to \left[ \begin{array}{l}
x = 1\\
{x^3} - 11{x^2} + 27x - 49 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1\\
x = 8,502201405
\end{array} \right.
\end{array}\)
