求K的值,已知abc的积不等于零,a/(b+c)=b/(c+a)=c/(a+b)=K.解题过程.

k=a/(b+c)=b/(c+a)=c/(a+b)
(1)当a+b+c不=0 时.
k=a/(b+c)=b/(a+c)=c/(a+b)
=(a+b+c)/[(b+c)+(a+c)+(a+b)]
=(a+b+c)/(2a+2b+2c)
=1/2
(2)当a+b+c=0 时.
a=-(b+c), b=-(a+c), c=-(a+b),
k=a/(b+c)=b/(a+c)=c/(a+b)
=-1