Question: When is raised to a positive integer power, the result can be written as A + Bo where A and B are Fibonacci numbers. You

When is raised to a positive integer power, the result can be written as A + Bo where A and B are Fibonacci numbers. You are asked to find $2, $3, 4 to gather evidence for the conjecture that each can be expresses in terms of A, B and as indicated . In other words, you should express each of the powers of as A + B$. Then guess (without calculating) A and B for $5 and explain the pattern emerging from your calculations. Investigate various ways to construct golden rectangles and show a geometric connection between them and Fibonacci numbers

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