Factorise $a^{2} + \dfrac{1}{a^{2}} + 2$ (for $a
e 0$).

Question

Factorise $a^{2} + \dfrac{1}{a^{2}} + 2$ (for $a 
e 0$).

Aicharya · Accepted Answer

$a^{2}+\dfrac{1}{a^{2}}+2 = a^{2}+2 \cdot a \cdot \dfrac{1}{a}+\left(\dfrac{1}{a}\right)^{2} = \left(a+\dfrac{1}{a}\right)^{2}$.

Factorise $a^{2} + \dfrac{1}{a^{2}} + 2$ (for $a \ne 0$).