Intermediate Algebra (11th edition)

SECTION 8.6 Solving Equations with Radicals 473

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29. 30.

31. 32.

33. 34.

35.Concept Check In solving the equation a student wrote the fol-
lowing for her first step. WHAT WENT WRONG?Solve the given equation correctly.

36.Concept Check In solving the equation a student wrote the
following for his first step. WHAT WENT WRONG?Solve the given equation correctly.

15 x+ 62 + 1 x+ 32 = 9

25 x+ 6 - 2 x+ 3 =3,

3 x+ 4 = 64 +x^2

23 x+ 4 = 8 - x,

2 r^2 + 9 r+ 15 - r- 4 = 0 2 m^2 + 3 m+ 12 - m- 2 = 0

2 x^2 + 12 x- 4 =x- 4 2 x^2 - 15 x+ 15 =x- 5

2 k^2 + 2 k+ 9 =k+ 3 2 x^2 - 3 x+ 3 =x- 1

29 - x=x+ 3 25 - x=x+ 1

x= 2 x^2 + 3 x+ 9 x= 2 x^2 - 4 x- 8

x= 2 x^2 + 4 x- 20 x= 2 x^2 - 3 x+ 18

32 x- 1 = 222 x+ 2 524 x+ 1 = 3210 x+ 25

22 x= 23 x+ 4 22 x= 25 x- 16

29 x- 4 = 28 x+ 1 24 x- 2 = 23 x+ 5

Solve each equation. See Examples 5 and 6.

For each equation, write the expressions with rational exponents as radical expressions, and
then solve, using the procedures explained in this section.

59. 
    
    
    
    60. 
        
    
    
    
    


60. 12 w- 12 2/3-w1/3= 0 62. 1 x^2 - 2 x 2 1/3-x1/3= 0

12 x- 92 1/2= 2 + 1 x- 82 1/2 13 w+ 72 1/2= 1 + 1 w+ 22 1/2

322 x+ 11 = 24 x+ 2 31 + 224 - 10 x= 23 x+ 5

23 - 3 p- 3 = 23 p+ 2 24 x+ 7 - 4 = 24 x- 1

23 p+ 4 - 22 p- 4 = 2 24 x+ 5 - 22 x+ 2 = 1

22 r+ 11 - 25 r+ 1 =- 1 23 x- 2 - 2 x+ 3 = 1

2 k+ 2 - 2 k- 3 = 1 2 r+ 6 - 2 r- 2 = 2

242 k- 5 + 4 = 0 248 z- 3 + 2 = 0

23 x- 8 + 2 = 0 23 r+ 1 + 1 = 0

24 x+ 12 = 243 x- 4 24 z+ 11 = 242 z+ 6

232 m- 1 = 23 m+ 13 232 k- 11 = 235 k+ 1

23 x^2 + 5 x+ 1 = 23 x^2 + 4 x 23 r^2 + 2 r+ 8 = 23 r^2 + 3 r+ 12

232 x+ 5 = 236 x+ 1 23 p+ 5 = 232 p- 4