# No use of any identities

Algebra Level 4

Let $$\alpha,\beta$$ be the roots of the equation $$x^2-x-1=0$$.

Let $$a_{2n}={\alpha}^{2n}+{\beta}^{2n}$$ where $$n\geq1$$ and $$n$$ is a natural number.

What is the value of $$a_{20}+a_{22}$$?

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