Question

Solve:
$a^6-7a^3-8=0$

Answer 1

Let $a^3=t$

$\Rightarrow t^2-7t-8=0$

$\Rightarrow t^2-8t+t-8=0$

$\Rightarrow t(t-8)+1(t-8)=0$

$\Rightarrow (t+1)(t-8)=0$

$\Rightarrow t=-1$ or $8$

$\Rightarrow a^3=-1$ or $a^3=8$

$\Rightarrow a=-1$ or $a=2$.