If we know that △ ABC is an obtuse triangle and the lengths of its three sides are continuous positive integers, then the cosine of its maximum internal angle is______ ．

If we know that △ ABC is an obtuse triangle and the lengths of its three sides are continuous positive integers, then the cosine of its maximum internal angle is______ ．


Let three sides be a, a + 1, a + 2 (a ＞ 0, a ∈ n *) and the maximum internal angle be α, then cos α = A2 + (a + 1) 2 − (a + 2) 22a (a + 1) = (a − 3) (a + 1) 2A (a + 1) = a − 32a ∵ △ ABC is an obtuse triangle, ∵ a − 32a ＜ 0 and a + A + 1 ＞ a + 2, ∵ a ＜ 3 and a ＞ 1, ∵ 1 ＜ a ＜ 3, ∵ a ∈ n *, ∵ a = 2, ∵ cos α ∵ 14

Elden Ring Premiere

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