已知△ABC的内角ABC的对边分别为abc,且abc成递减的等差数列,若A等于2C,则a
2个回答
展开全部
已知△ABC的内角ABC的对边分别为abc,且abc成递减的等差数列,若升败A等于2C,则a
abc成递减的等差数列
a-b=b-c
a+c=2b
A等于2C
a/sinA=c/sinC
a/sin2C=c/sinC
a/2sinCcosC=c/sinC
cosC=a/2c
cosC=(a^2+b^2-c^2)/2ab
=(a^2+[(a+c)/2]^2-c^2)/[2a(a+c)/吵源颤2]
=(5a^2+2ac-3c^2)/4a(a+c)
=(5a-3c)/4a
a/2c=(5a-3c)/4a
2a^2-5ac+3c^2=0
(2a-3c)(a-c)=0
abc成递减裂液的等差数列
a-c≠0
2a-3c=0
a=3c/2
abc成递减的等差数列
a-b=b-c
a+c=2b
A等于2C
a/sinA=c/sinC
a/sin2C=c/sinC
a/2sinCcosC=c/sinC
cosC=a/2c
cosC=(a^2+b^2-c^2)/2ab
=(a^2+[(a+c)/2]^2-c^2)/[2a(a+c)/吵源颤2]
=(5a^2+2ac-3c^2)/4a(a+c)
=(5a-3c)/4a
a/2c=(5a-3c)/4a
2a^2-5ac+3c^2=0
(2a-3c)(a-c)=0
abc成递减裂液的等差数列
a-c≠0
2a-3c=0
a=3c/2
追问
为什么我的这个结果不对呢?帮我看一下。 a/sinA=c/sinC => 2cosC=a/c , 2b=a+c c²=a²+b²-2abcosC c²=(a+c)²/4-a²(a+c)/2c =>3c³-2ac²=3ca²-2a³ c²(3c-2a)=a²(3c-2a) c²=a²?? 这是怎么回事?
追答
c^2(3c-2a)=a^2(3c-2a)
c^2(3c-2a)-a^2(3c-2a)=0
(c a)(c-a)(3c-2a)=0
c a≠0
c-a≠0
3c-2a=0
a=3c/2
展开全部
已知的内角的△ABC ABC的边ABC和ABC降序等差数列,如果A是等于茄返2C,
ABC到下降的等差数列
AB = BC
A + C = 2B
等于2C
A /新浪= C /颤绝饥 SINC
a/sin2C = C / SINC
a/2sinCcosC = C / SINC
COSC = a/2c
COSC =(A ^ 2 + B ^ 2-C ^ 2)/ 2AB
=(A ^ 2 + [(A + C)/ 2] ^ 2-C ^ 2) / [2A(A + C)/ 2]
=(5A ^ 2 +2 AC-3C ^ 2)/ 4A(A + C)
=(5A-3C)/ 4A <BR / a/2c =(5A-3C)/ 4A
2A ^ 2-5AC +3 C ^ 2 = 0
(宏闹2A-3C)(AC)= 0
ABC则会减少等差数列
AC≠0
2A-3C = 0
= 3C / 2
ABC到下降的等差数列
AB = BC
A + C = 2B
等于2C
A /新浪= C /颤绝饥 SINC
a/sin2C = C / SINC
a/2sinCcosC = C / SINC
COSC = a/2c
COSC =(A ^ 2 + B ^ 2-C ^ 2)/ 2AB
=(A ^ 2 + [(A + C)/ 2] ^ 2-C ^ 2) / [2A(A + C)/ 2]
=(5A ^ 2 +2 AC-3C ^ 2)/ 4A(A + C)
=(5A-3C)/ 4A <BR / a/2c =(5A-3C)/ 4A
2A ^ 2-5AC +3 C ^ 2 = 0
(宏闹2A-3C)(AC)= 0
ABC则会减少等差数列
AC≠0
2A-3C = 0
= 3C / 2
本回答被网友采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是?
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询