Solutions to Try Its

1. [latex]\frac{1}{4}[/latex]

2. [latex]25[/latex]

3. [latex]\{-1\}[/latex]

4. [latex]x=0[/latex], [latex]x=\frac{1}{2}[/latex], [latex]x=-\frac{1}{2}[/latex]

5. [latex]x=1[/latex]; extraneous solution [latex]x=-\frac{2}{9}[/latex]

6. [latex]x=-2[/latex]; extraneous solution [latex]x=-1[/latex]

7. [latex]x=-1[/latex], [latex]x=\frac{3}{2}[/latex]

8. [latex]x=-3,3,-i,i[/latex]

9. [latex]x=2,x=12[/latex]

10. [latex]x=-1[/latex], [latex]x=0[/latex] is not a solution.

Solutions to Odd-Numbered Exercises

1. This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.

3. He or she is probably trying to enter negative 9, but taking the square root of [latex]-9[/latex] is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in [latex]-27[/latex].

5. A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.

7. [latex]x=81[/latex]

9. [latex]x=17[/latex]

11. [latex]x=8, x=27[/latex]

13. [latex]x=-2,1,-1[/latex]

15. [latex]y=0, \frac{3}{2}, \frac{-3}{2}[/latex]

17. [latex]m=1,-1[/latex]

19. [latex]x=\frac{2}{5}[/latex]

21. [latex]x=32[/latex]

23. [latex]t=\frac{44}{3}[/latex]

25. [latex]x=3[/latex]

27. [latex]x=-2[/latex]

29. [latex]x=4,\frac{-4}{3}[/latex]

31. [latex]x=\frac{-5}{4},\frac{7}{4}[/latex]

33. [latex]x=3,-2[/latex]

35. [latex]x=-5[/latex]

37. [latex]x=1,-1,3,-3[/latex]

39. [latex]x=2,-2[/latex]

41. [latex]x=1,5[/latex]

43. All real numbers

45. [latex]x=4,6,-6,-8[/latex]

47. 10 in.

49. 90 kg