∵b加c分之a(chǎn)等于a加c分之b等于a加b分之c等于k
∴a/k=(b+c)b=(a+c)kc=(a+b)k
∴a/(ak+ck+ak+bk)=k
a/[2ak+k(b+c)]=k
a/(2ak+k*a/k)=k
a/(2ak+a)=k
1/(2k+1)=k
1=2k²+k
2k²+k-1=0
(2k-1)(k+1)=0
2k-1=0 k+1=0
∴k=1/2
或k=-1