[tex]\text{Given that ,}~~ \left(a - \dfrac 1a \right) =3\\\\\\ \text{We know that,} ~~4ab =(a+b)^2 -(a-b)^2\\\\\\4 \cdot a \cdot \dfrac 1a = \left(a + \dfrac 1a \right)^2 - \left(a - \dfrac 1a \right)^2\\\\\\\implies \left(a + \dfrac 1a \right)^2 = 4 + \left(a - \dfrac 1a \right)^2 = 4+3^2 = 4+9 =13\\\\\text{Proved}.[/tex]
