Question

b+c分之a=c+a分之b=a+b分之c=k,则k的值是_____

Answer 1

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