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The Golden Ratio is one of the roots of the equation x^2-x-1=0 and the nth Fibonacci number isF_n={1\over\sqrt5}(\alpha^n-\beta^n) where \alpha and \beta are solutions of the quadratic equation x^2-x-1=0 and \alpha > \beta hence the many connections between Fibonacci numbers and the Golden Ratio.
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The Golden Ratio is one of the roots of the equation x^2-x-1=0 and the nth Fibonacci number isF_n={1\over\sqrt5}(\alpha^n-\beta^n) where \alpha and \beta are solutions of the quadratic equation x^2-x-1=0 and \alpha > \beta hence the many connections between Fibonacci numbers and the Golden Ratio.
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