Recent questions tagged algebra

​​​​​​​$\bigoplus$ and $\bigodot$ are two operators on numbers $\text{p}$ and $\text{q}$ such that $p \bigoplus q=\dfrac{p^{2}+q^{2}}{pq}$ and $p \bigodot q=\dfrac{p^{2}}...

If $x^{2}+ x - 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$?$1$$5$$7$$9$