\[\left( x^{2} + 27x - 57 \right)^{2} = \left( x^{2} - 3x + 1 \right)^{2}\]
\[1)\ x^{2} + 27x - 57 = x^{2} - 3x + 1\]
\[27x + 3x = 1 + 57\]
\[30x - 58 = 0\]
\[2 \cdot (15x - 29) = 0\]
\[15x = 29\]
\[x = \frac{29}{15}.\]
\[2)\ x^{2} + 27x - 57 = - x^{2} + 3x - 1\]
\[2x^{2} + 24x - 56 = 0\]
\[2 \cdot \left( x^{2} + 15x - 28 \right) = 0\]
\[2 \cdot (x - 2)(x + 14) = 0\]
\[x = 2;\ \ \ x = - 14\]
\[Ответ:x = \frac{29}{15};\ \ x = 2;\ \ x = - 14.\]