\(\begin{array}{l} {({x^2} - x + 1)^x} > 1 \Leftrightarrow {({x^2} - x + 1)^x} > {({x^2} - x + 1)^0}\\ \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} {x^2} - x + 1 > 1\\ x > 0 \end{array} \right.\\ \left\{ \begin{array}{l} 0 < {x^2} - x + 1 < 1\\ x < 0 \end{array} \right. \end{array} \right. \Leftrightarrow x > 1. \end{array}\)