勾股逆定理的推广

THE EXTENSION OF THE PYTHAGOREAN INVERSE THEOREM

用导数方法对勾股逆定理进行了推广，得到了如下结果：在△ABC中，若△a^x＋b^x＝c^x，其中x∈R－［0，1」，则1）当x∈（－∞，0）∪（1，2］时，Cmax＝；2）当x∈［2，＋∞）时，Cmin＝．此外，给出了上述结果的两个推论及其应用．

Pythagorean inverse theorem is generalized by using derivatives. The followingresult is obtained ,In △ABC, let , where x∈ R － [0, 1], Then Cmax＝ arccos if x ∈ (－ ∞，0) ∪ [＋ 2，＋∞); Cmin ＝ arccos if x ∈ [2, ＋ ∞). Two corol-laries and some examples are also given here.