Question

2013人教版七年级上册数学名师测控27页答案

Answer 1

证明：a+b+c=180°,2b=a+c=180°-b,则b=60°；

则由余弦定理可知：cosb=(a²+c²-b²)/(2ac)=cos60°=1/2

即(a²+c²-b²)/(2ac)=1/2

a²+c²-b²=ac

a²+c²=ac+b²

a²+c²+ab+bc=ac+b²+ab+bc

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

[c(b+c)+a(a+b)]/[(a+b)(b+c)]=1

[c/(a+b)]+[a/(b+c)]=1

[c/(a+b)]+1+[a/(b+c)]+1=1+1+1

[c/(a+b)]+[(a+b)/(a+b)]+[a/(b+c)]+[(b+c)/(b+c)]=3

[(a+b+c)/(a+b)]+[(a+b+c)/(b+c)]=3

[1/(a+b)]+[1/(b+c)]=3/(a+b+c)