Question

三角形ABC中，内角A,B,C对边分别为a，b，c，c=2，C=3/π，面积等于根号3，求a，b

Answer 1

c=2，C=π/3
c^2 = a^2+b^2-2abcosπ/3 = a^2+b^2-2ab*1/2 = a^2+b^2-ab = 2^2 = 4......(1)

面积等于根号3
S = 1/2absinC = 1/2absinπ/3 = 根号3/4 ab = 根号3
ab=4......(2)

由（1）得：
(a+b)^2-3ab =4 ......(3)
将(2)代入（3）
(a+b)^2-3*4 =4
(a+b)^2 =16
a+b = 4
b=4-a
将b=4-a代入ab=4
a(4-a)=4
a^2-4a+4=0
(a-2)^2=0
a=2
b=4-a=2