Answer:

Chapter 1

1.1 {x : x3 − 5x2 + 11x + 6 = 0}, the set of the first three positive whole numbers

and {1, 2, 3} are some answers.

1.2 72 = 23 · 32, 84 = 22 · 3 · 7, (72, 84) = 22 · 3 = 12. 56 = 23 · 7, 42 = 2 · 3 · 7,

(56, 42) = 2 · 7 = 14.

1.3 1, 0, 1,x3, −0.5, 0.04.

1.4 t−2/t−3 = t3/t2 = t; y5−2 = y3; (4x−2)(3x4) = 12x4−2 = 12x2.

1.5 32 = 9 so log3 9 = 2; 53 = 125 so log5 125 = 3; √4 = 2 so log4 2 = 1

2 .

1.6 9

√3 = 32 · 3

1

2 so log3 9

√3 = 5

2 and log3 (9

√3)5 = 5 log3 9

√3 = 25

2 or 12.5.

1.7 2, −2, 5, −4, 3.1, 4.4.

1.8 -

5

i=3 i(i − 1) = 3 · 2 + 4 · 3 + 5 · 4 = 6 + 12 + 20 = 38; -

6

i=2 i =

2 + 3 + 4 + 5 + 6 = 20.

1.9 1 + 3 + 5 + 7 + 9 = -

5

i=1 2i − 1; 8 + 27 + 64 + 125 = -

5

i=2 i3.

1.11 3+7+···+43 = -

11

i=1 4i − 1 = 4·

-

11

i=1 i−11 = 4· 12·11

2 −11 = 264−11 =

253.

1.12 (144)5 = 52+4·5+4 = 49, (203)7 = 2·72+3 = 101, (112)3 = 32+3+2 =

14.

1.13 (0.242)5 = 2 · 5−1 + 4 · 5−2 + 2 · 5−3 = 0.4 + 0.16 + 0.016 = 0.576 so (using

the preceding answer) (144.242)5 = 49.576.

1.14

5 54

5 10 + 4

2 + 0

54 = (204)5

6 103

6 17 + 1

2 + 5

103 = (251)6.