Ridicăm la pătrat:
[tex]\bigg(a + \dfrac{1}{a}\bigg)^{2} = {a}^{2} + 2 \times a \times \dfrac{1}{a} + \dfrac{1}{ {a}^{2} }[/tex]
[tex]{5}^{2} = {a}^{2} + 2 + \dfrac{1}{ {a}^{2} } \implies {a}^{2} + \dfrac{1}{ {a}^{2} } = 25 - 2 \\ [/tex]
[tex]\implies {a}^{2} + \dfrac{1}{ {a}^{2} } = 23[/tex]
