$x^{15}=x$
$⇒x= 1 ; 0$
$(2x+1)³=125$
$⇔2x+1=5$
$⇔2x=4$
$⇔x=4$
$(x-5)^{4}=(x-5)^{6}$
⇔\(\left[ \begin{array}{l}x-5=0\\x-5=1\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=5\\x=6\end{array} \right.\)
$x^{2006}=x^{2}$
⇔\(\left[ \begin{array}{l}x=±1\\x=0\end{array} \right.\)