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4个算式是等价的。
Minimize[{((a^2 + b^2) Sin[\[Pi]/3])/2, a^2 + b^2 == c^2 + (3 - a)^2 - 2 c (3 - a) * 3/5 == (4 - b)^2 + (5 - c)^2 - 2 (4 - b) (5 - c) * 4/5}, {a, b, c}]
Minimize[{((a^2 + b^2) Sqrt[3])/4, a^2 + b^2 == c^2 + (3 - a)^2 - (6 c (3 - a))/5 == (4 - b)^2 + (5 - c)^2 - (8 (4 - b) (5 - c))/5}, {a, b, c}]
Minimize[{((a^2 + b^2) Sqrt[3])/4, c^2 == b^2 + 6 a - 9 + (6 c (3 - a))/5 == a^2 + 8 b + 10 c - 41 + (8 (4 - b) (5 - c))/5}, {a, b, c}]
Minimize[{((a^2 + b^2) Sqrt[3])/4, 5 c^2 - 18 c + 45 == 5 b^2 - 6 a c + 30 a == 5 a^2 + 8 b c}, {a, b,c}]
{36/193 (-36 + 25 Sqrt[3]), {a -> 6/193 (-8 + 27 Sqrt[3]), b -> 6/193 (-69 + 64 Sqrt[3]), c -> 15/193 (3 + 14 Sqrt[3])}} |
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