Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.6 - Segments Divided Proportionally - Exercises - Page 267: 25

Answer

x does not exist

Work Step by Step

Using proportions, we obtain: $\frac{x-6}{2-x} = \frac{3}{x+2} \\ x^2 -4x -12 = 6 - 3x \\ x^2 -x - 18 = 0 $ We use the quadratic formula to obtain: $ x = \frac{1 \pm \sqrt{73}}{2}$ Since RS equals x-6, this value must be greater than 6. However, both solutions are less than 6, so x does not exist.
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