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)
Explanation:
