Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 8 Rational Functions - 8.6 Solve Rational Equations - 8.6 Exercises - Problem Solving - Page 594: 37



Work Step by Step

According to the exercise: $\frac{w}{l}=\frac{l}{l+w}$ and $w=1$. Hence here: $\frac{1}{l}=\frac{l}{l+1}\\l+1=l^2\\l^2-l-1=0$ By the quadratic formula: $l=\frac{1+\sqrt5}{2}$ (the other solution is negative, which is impossible), hence the golden ratio is: $\frac{1}{\frac{1+\sqrt5}{2}}=\frac{2}{1+\sqrt5}$
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