Intermediate Algebra (11th edition)

33.Rusty and Nancy Brauner are planting flats of spring flowers. Working alone, Rusty
would take 2 hr longer than Nancy to plant the flowers. Working together, they do the
job in 12 hr. How long (to the nearest tenth) would it have taken each person working
alone?

34.Joel Spring can work through a stack of invoices in 1 hr less time than Noel White can.
Working together they take hr. How long (to the nearest tenth) would it take each per-
son working alone?

35.Two pipes together can fill a tank in 2 hr. One of the pipes, used alone, takes 3 hr longer
than the other to fill the tank. How long would each pipe take to fill the tank alone?

36.A washing machine can be filled in 6 min if both the hot and cold water taps are fully
opened. Filling the washer with hot water alone takes 9 min longer than filling it with
cold water alone. How long does it take to fill the washer with cold water?

Solve each equation. Check your solutions. See Example 4.

37. 
    
    
    
    38. 
        
        
        
        39. 
            
        
        
        
        
    
    
    
    


38. 
    
    
    
    41. 
        
        
        
        42. 
            
        
        
        
        
    
    
    
    

43. 44. 45.

46. 47. 48.

Solve each equation. Check your solutions. See Examples 5 –7.

49. 
    
    
    
    50. 
        
    
    
    
    


50. 
    
    
    
    52. 
        
    
    
    
    


51. 
    
    
    
    54. 
        
    
    
    
    


52. 
    
    
    
    56. 
        
    
    
    
    


53. 
    
    
    
    58. 
        
    
    
    
    


54. 
    
    
    
    60. 
        
    
    
    
    


55. 
    
    
    
    62. 
        
    
    
    
    


56. 
    
    
    
    64. 
        
    
    
    
    


57. 
    
    
    
    66. 
        
    
    
    
    

67. 68.

The equations in Exercises 69– 82 are not grouped by type. Solve each equation. Exercises 81
and 82 require knowledge of complex numbers. See Examples 1 and 4 –7.

69. 
    
    
    
    70. 
        
    
    
    
    

71. 72.

73. 74.

75. 76.

77. 78.

79. 80.

81. 2 x^4 +x^2 - 3 = 0 82. 4 x^4 + 5 x^2 + 1 = 0

2 x^4 - 9 x^2 =- 2 8 x^4 + 1 = 11 x^2

6 = 712 w- 32 -^1 + 312 w- 32 -^2 x^6 - 10 x^3 =- 9

2 m^6 + 11 m^3 + 5 = 0 8 x^6 + 513 x^3 + 64 = 0

2 A 1 + 2 rB 1 x^2 +x 22 + 12 = 81 x^2 +x 2

2

= 13 A 1 + 2 rB- 6

22 x+ 3 = 2 + 2 x- 2 2 m+ 1 =- 1 + 22 m

ax-

1

2

b

2

+ 5 ax-

1

2

12 x^4 - 11 x^2 + 2 = 0 b - 4 = 0

2 - 61 z- 12 -^2 = 1 z- 12 -^13 - 21 x- 12 -^1 = 1 x- 12 -^2

3 -

7

2 p+ 2

=

6

12 p+ 222

2 +

5

3 x- 1

=

- 2

13 x- 122

4 x4/3- 13 x2/3+ 9 = 0 9 t4/3- 25 t2/3+ 16 = 0

r2/3+r1/3- 12 = 0 3 x2/3-x1/3- 24 = 0

x2/3+x1/3- 2 = 0 x2/3- 2 x1/3- 3 = 0

31 m+ 422 - 8 = 21 m+ 42 1 t+ 522 + 6 = 71 t+ 52

1 x+ 322 + 51 x+ 32 + 6 = 0 1 x- 422 + 1 x- 42 - 20 = 0

x^4 + 48 = 16 x^2 z^4 + 72 = 17 z^2

4 q^4 - 13 q^2 + 9 = 0 9 x^4 - 25 x^2 + 16 = 0

x^4 - 29 x^2 + 100 = 0 x^4 - 37 x^2 + 36 = 0

• x=
  B

3 x+ 7

4

• x=
  B

8 - 2 x

3

r=

B

20 - 19 r

6

x=

B

6 - 13 x

5

t+ 2 t = 12 p- 22 p= 8

4 x= 26 x+ 1 3 x= 216 - 10 x 4 t= 28 t+ 3

x= 27 x- 10 z= 25 z- 4 2 x= 211 x+ 3

(^112)

SECTION 9.3 Equations Quadratic in Form 521