Question
Solve equation by factorization :$ a^2x^2 + 2ax + 1 = 0, a \neq 0$
✓
Answer
$ a^2 x^2+2 a x+1=0$
$\Rightarrow a^2 x^2+a x+a x+1=0$
$\Rightarrow a x(a x+1)+1(a x+1)=0$
$\Rightarrow a x(a x+1)(a x+1)=0$
$\Rightarrow(a x+1)^2=0$
$\therefore a x+1=0$
$\Rightarrow a x=-1$
$\Rightarrow x=-\frac{1}{a}$
Hence $x =-\frac{1}{a}, \frac{1}{a}$.
$\Rightarrow a^2 x^2+a x+a x+1=0$
$\Rightarrow a x(a x+1)+1(a x+1)=0$
$\Rightarrow a x(a x+1)(a x+1)=0$
$\Rightarrow(a x+1)^2=0$
$\therefore a x+1=0$
$\Rightarrow a x=-1$
$\Rightarrow x=-\frac{1}{a}$
Hence $x =-\frac{1}{a}, \frac{1}{a}$.
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