Question

Factorise : ${\displaystyle x^2+\frac{a^2+1}{a}x+1}$

Answer 1

${\displaystyle x^2+\frac{a^2+1}{a}x+1=0}$

∴ ${\displaystyle x^2+ax+\frac{1}{a}x+1=0}$

∴ ${\displaystyle x(x+a)+\frac{1}{a}(x+a)=0}$

∴ ${\displaystyle (x+a)(x+\frac{1}{a})=0}$