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Explanation & Answer
L(k)= L(k-1)+ L(k-2)
=α^(k-1)+β^(k-1) + (α +β)
= α^(k-2) (α+1)+β^(k-2) (β+2)
=α^(k-2) (α̂²)+β^(k-2) (β̂²)
=α^k+β^k
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