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我喜欢把答案先找出来,慢慢琢磨为什么会是这样?想不通就先摆一摆(不要有负担)。
Minimize[{a/(b + c) + b/(c + a) + c/(a + b), a > 0, b > 0, c > 0}, {a, b, c}]
{3/2, {a -> 1, b -> 1, c -> 1}}
NMinimize[{a/(b + c) + b/(c + d) + c/(d + a) + d/(a + b), a > 0, b > 0, c > 0, d > 0},
{2., {a -> 2.30637, b -> 0.732111, c -> 2.30637, d -> 0.732111}}
NMinimize[{a/(b + c) + b/(c + d) + c/(d + e) + d/(e + a) + e/(a + b), a > 0, b > 0, c > 0,
{2.5, {a -> 0.734372, b -> 0.734372, c -> 0.734372, d -> 0.734372, e -> 0.734372}}
NMinimize[{a/(b + c) + b/(c + d) + c/(d + e) + d/(e + f) + e/(f + a) +f/(a + b), a > 0, b > 0,
{3., {a -> 1.44065, b -> 0.808194, c -> 1.44065, d -> 0.808194, e -> 1.44065, f -> 0.808194}}
NMinimize[{a/(b + c) + b/(c + d) + c/(d + e) + d/(e + f) + e/(f + g) +f/(g + a) + g/(a + b),
{3.5, {a -> 1.72387, b -> 1.72387, c -> 1.72387, d -> 1.72387, e -> 1.72387, f -> 1.72387,
NMinimize[{a/(b + c) + b/(c + d) + c/(d + e) + d/(e + f) + e/(f + g) + f/(g + h) + g/(h + a) +
{4., {a -> 0.947866, b -> 1.40559, c -> 0.947866, d -> 1.40559, e -> 0.947866, f -> 1.40559, |
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