Question

试证：在△ABC中,∠C=60°,试证b/a+c + a/b+c = 1

Answer 1

过点A作AM垂直AB于点M,

∵∠C=60°,∴CM=b/2,AM＝√3b/2

∴(√3b/2)^2+(a-b/2)^2=c^2

a^2-ab+b^2=c^2

b(b+c)+a(a+c)=ab+ac+bc+c^2

b(b+c)+a(a+c)=(a+c)(b+c)

即b/(a+c)+a/(b+c)=1