College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 51


$x=\left\{ \dfrac{1-\sqrt{5}}{2},\dfrac{1+\sqrt{5}}{2}\right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ x^2-x-1=0 ,$ use the Quadratic Formula. $\bf{\text{Solution Details:}}$ In the equation above, $a= 1 ,$ $b= -1 ,$ and $c= -1 .$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then \begin{array}{l}\require{cancel} x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(-1)(-1)}}{2(1)} \\\\ x=\dfrac{1\pm\sqrt{1+4}}{2} \\\\ x=\dfrac{1\pm\sqrt{5}}{2} .\end{array} The solutions are $ x=\left\{ \dfrac{1-\sqrt{5}}{2},\dfrac{1+\sqrt{5}}{2}\right\} .$
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