1. In a radical equation, what does it mean if a number is an extraneous solution?
2. Explain why possible solutions must be checked in radical equations.
3. Your friend tries to calculate the value −923 and keeps getting an ERROR message. What mistake is he or she probably making?
4. Explain why ∣2x+5∣=−7 has no solutions.
5. Explain how to change a rational exponent into the correct radical expression.
For the following exercises, solve the rational exponent equation. Use factoring where necessary.
6. x32=16
7. x43=27
8. 2x21−x41=0
9. (x−1)43=8
10. (x+1)32=4
11. x32−5x31+6=0
12. x37−3x34−4x31=0
For the following exercises, solve the following polynomial equations by grouping and factoring.
13. x3+2x2−x−2=0
14. 3x3−6x2−27x+54=0
15. 4y3−9y=0
16. x3+3x2−25x−75=0
17. m3+m2−m−1=0
18. 2x5−14x3=0
19. 5x3+45x=2x2+18
For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions.
20. 3x−1−2=0
21. x−7=5
22. x−1=x−7
23. 3t+5=7
24. t+1+9=7
25. 12−x=x
26. 2x+3−x+2=2
27. 3x+7+x+2=1
28. 2x+3−x+1=1
For the following exercises, solve the equation involving absolute value.
29. ∣3x−4∣=8
30. ∣2x−3∣=−2
31. ∣1−4x∣−1=5
32. ∣4x+1∣−3=6
33. ∣2x−1∣−7=−2
34. ∣2x+1∣−2=−3
35. ∣x+5∣=0
36. −∣2x+1∣=−3
For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring.
37. x4−10x2+9=0
38. 4(t−1)2−9(t−1)=−2
39. (x2−1)2+(x2−1)−12=0
40. (x+1)2−8(x+1)−9=0
41. (x−3)2−4=0
For the following exercises, solve for the unknown variable.
42. x−2−x−1−12=0
43. ∣x∣2=x
44. t25−t5+1=0
45. ∣x2+2x−36∣=12
For the following exercises, use the model for the period of a pendulum, T, such that T=2πgL, where the length of the pendulum is L and the acceleration due to gravity is g.
46. If the acceleration due to gravity is 9.8m/s2 and the period equals 1 s, find the length to the nearest cm (100 cm = 1 m).
47. If the gravity is 32s2ft and the period equals 1 s, find the length to the nearest in. (12 in. = 1 ft). Round your answer to the nearest in.
For the following exercises, use a model for body surface area, BSA, such that BSA=3600wh, where w = weight in kg and h = height in cm.
48. Find the height of a 72-kg female to the nearest cm whose BSA=1.8.
49. Find the weight of a 177-cm male to the nearest kg whose BSA=2.1.
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College Algebra.Provided by: OpenStaxAuthored by: OpenStax College Algebra.Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface.License: CC BY: Attribution.