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]{a}^{2} + 2 + \dfrac{1}{ {a}^{2} } = 9 \implies {a}^{2} + \dfrac{1}{ {a}^{2} } = 7[/tex]
Ridicăm din nou la pătrat:
[tex]\bigg( {a}^{2} + \dfrac{1}{{a}^{2}}\bigg)^{2} = ({a}^{2})^{2} + 2 \times {a}^{2} \times \dfrac{1}{{a}^{2}} + \dfrac{1}{ ({a}^{2})^{2} } \\ [/tex]
[tex]{a}^{4} + 2 + \dfrac{1}{ {a}^{4} } = 49 \implies \bf {a}^{4} + \dfrac{1}{ {a}^{4} } = 47 \\ [/tex]
