Finding the exact value of the Golden Ratio using the quadratic formula.

by: Kelli Nipper

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Let the short side of a golden rectange = 1, and the long side be x. The following proportion must hold:

Cross multiplying gives:

Using the quadratice formula yields the roots:

The first being the exact value of the Golden Ratio, and the second being the reciprocal and conjugate of the Golden Ratio.

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