Answer
$a=-1, 1, i$
Work Step by Step
$a^6-a^2=a^4-1$
$a^6-a^2-a^4+1=a^4-1-a^4+1$
$a^6-a^4-a^2+1=0$
$a^4(a^2-1)-(a^2-1)=0$
$(a^4-1)(a^2-1)=0$
$a^4-1=0$
$(a^2+1)(a^2-1)=0$
$a^2+1=0$
$a^2+1-1=0-1$
$a^2=-1$
$\sqrt {a^2} = \sqrt {-1}$
$a = i$
$a^2-1=0$
$a^2-1+1=0+1$
$a^2=1$
$\sqrt {a^2} = \sqrt {1}$
$a=±1$
