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ATQ, a2c + ab2- ac2- ba2 + bc2- cb2 + abc (a - b)(b - c)(c - a) + abc Minimum value, (2 - 5)(5 - 8)(8 - 2) + 2 × 5 × 8 = (- 3)(- 3) × 6 + 80 = 54 + 80 = 134 Maximum value, (4 - 7)(7 - 10)(10 - 4) + 4 × 7 × 10 = (- 3)(- 3) × 6 + 280 = 54 + 280 = 334 Quantity II (ab + bc)(c2- b2- c2) Minimum value, (2 × 5 + 5 × 8) × (82 - 52 - 22) = (10 + 40) × (64 - 25 - 4) = 50 × 35 = 1750 Maximum value, (4 × 7 + 7 × 10) × (102 - 72 - 42) = (28 + 70) × (100 - 49 - 16) = 98 × 35 = 3430 Hence, Quantity I < Quantity II .
56. 23 45 89 177 363 705
...Find the maximum number of trees which can be planted, 25 meters apart, on the two sides of a straight road 2125 meters long
49 84 119 154 189 ?
48 83 118 153 188 ?
800 400 600 1500 ? 23625
...5, 14, 41, 122, 365, 1094, ?
102, 246, 442, 698, 1022, ?
61, 48, ?, 35, 87, 22
48 24 72 18 90 ?
6000 3002 1503 ? 378.75 191.375 97.6875
...