Basic Technical Mathematics, 11th Edition

Exercises 14.4, page 417

1. 1. ${\displaystyle \frac{13}{12}}$

2. 3. 10

3. 5. 12

4. 7. 3

5. 9. ${\displaystyle \frac{2}{3}}$

6. 11. $\hspace{0.17em}-\hspace{0.17em}1$

7. 13. 15

8. 15. 4, 9

9. 17. $\hspace{0.17em}\pm \hspace{0.17em}6$

10. 19. 12 (Extraneous root introduced in squaring both sides of $\sqrt{x\hspace{0.17em}+\hspace{0.17em}4}\hspace{0.17em}=\hspace{0.17em}x\hspace{0.17em}-\hspace{0.17em}8\hspace{0.17em}.\hspace{0.17em}$)

11. 21. 16

12. 23. $0\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{1}{9}}$

13. 25. $\hspace{0.17em}-\hspace{0.17em}1\hspace{0.17em},\hspace{0.17em}7$

14. 27. 0

15. 29. 5

16. 31. 25

17. 33. 8

18. 35. 4

19. 37. 4

20. 39. 16

21. 41. $x\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em};\hspace{0.17em}$ For $x\hspace{0.17em}=\hspace{0.17em}5\hspace{0.17em},\hspace{0.17em}$ squaring $3\hspace{0.17em}-\hspace{0.17em}x$ is squaring a negative number. A different extraneous root is introduced.

22. 43. $\hspace{0.17em}-\hspace{0.17em}r\hspace{0.17em}\pm \hspace{0.17em}\sqrt{r^2\hspace{0.17em}+\hspace{0.17em}{R}^2}$

23. 45. $r_1^2\hspace{0.17em}=\hspace{0.17em}{(kC\hspace{0.17em}+\hspace{0.17em}A\hspace{0.17em}-\hspace{0.17em}\sqrt{R_1^2\hspace{0.17em}-\hspace{0.17em}{R}_2^2})}^2\hspace{0.17em}+\hspace{0.17em}{r}_2^2$

24. 47. $228,000

25. 49. 9.2 km

26. 51. 1.6 mi