# Solutions

1. 1
(.5 + .5) × .5 = .5
(0.5 + 1) × 1 = 1.5
(1.5 + 1.5) × 1.5 = 4.5
(4.5 + 2) × 2 = 13
(13 + 2.5 ) × 2.5 = 38.75

2. 2
2 × 6.5 = 13
3 × 6 = 18
4 × 5.5 = 22
5 × 5 = 25
6 × 4.5 = 27
7 × 4 = 28
8 × 3.5 = 28

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1 + 1^3 = 2
2 + 2^3 = 10
3 + 3^3 = 30
4 + 4^3 = 68
5 + 5^3 = 130
6 + 63 = 222
7 + 73 = 350

4. 3
11 × 2 + 2 = 24
24 ÷ 2 + 4 = 16
16 × 2+ 6 = 38
38 ÷ 2 + 8 = 27
27 × 2 + 10 = 64
64 ÷ 2 + 12 = 44

5. 2
821 – 19^2 = 460
460 + 17^2 = 749
749 – 13^2 = 580
580 + 11^2 = 701
701 – 7^2 = 652
652 + 52 = 677

6. 4
1. 12 x^2 – 6x – 7x + 21 = 0
x = 3, 7/2
2. 2y^2 – 7y + 3 = 0
y = 3, 1/2

7. 2
1. x^2 – 12x + 35 = 0
x = 7 or 5
2. 6y^2 + 11y + 3 = 0
y = -1/3, -3/2
x > y

8. 5
1. 2x^2 – 17 x + 21= 0
or, 2x^2 – 14 x – 3 x + 21 = 0
x = 7 or 3/2
2. y^2 – 15 y + 56 = 0
y^2 – 8y – 7y + 56 = 0
y(y – 8) – 7 (y – 8) = 0
(y – 8) (y – 7)
y = 8, 7
x <= y

9. 1
1. x^2 + 2x – 8 = 0
x^2 + 4 x – 2 – 8 = 0
x = – 4 or +2
2. 2 y^2 – 15 y + 28 = 0
y = 7/2, 4
x < y

10. 3
1. x = 1/3
2. 9y^2 – 6y + 1 = 0
(3y – 1)^2 = 0
y = 1/3
x = y

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