在三角形ABC中,三个内角A,B,C的对边分别为a.b.c且A,B,C成等差数列.a.b.c成等比数列,求证三角形ABC为等
人气:459 ℃ 时间:2019-11-05 04:26:22
解答
A,B,C成等差数列==>A+C=2B=180°-B ,B=60°
a.b.c成等比数列===>b^2=ac =a^2+c^2-2accosB=a^2+c^2-ac
(a-c)^2=0,a=c所以三角形ABC为等边三角形
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