Exercises 14.4, page 417

1. $\frac{13}{12}$ $\frac{13}{12}$
3. 10
5. 12
7. 3
9. $\frac{2}{3}$ $\frac{2}{3}$
11. $- 1$ $- 1$
13. 15
15. 4, 9
17. $\pm 6$ $\pm 6$
19. 12 (Extraneous root introduced in squaring both sides of $\sqrt{x + 4} = x - 8 .$ $\sqrt{x + 4} = x - 8 .$ )
21. 16
23. $0, \frac{1}{9}$ $0, \frac{1}{9}$
25. $- 1, 7$ $- 1, 7$
27. 0
29. 5
31. 25
33. 8
35. 4
37. 4
39. 16
41. $x = 2;$ $x = 2;$ For $x = 5,$ $x = 5,$ squaring $3 - x$ $3 - x$ is squaring a negative number. A different extraneous root is introduced.
43. $- r \pm \sqrt{r^{2} + R^{2}}$ $- r \pm \sqrt{r^{2} + R^{2}}$
45. $r_{1}^{2} = {(k C + A - \sqrt{R_{1}^{2} - R_{2}^{2}})}^{2} + r_{2}^{2}$ $r_{1}^{2} = {(k C + A - \sqrt{R_{1}^{2} - R_{2}^{2}})}^{2} + r_{2}^{2}$
47. $228,000
49. 9.2 km
51. 1.6 mi

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Table of Contents for Exercises 14.4, page 417