已知a/(b+2c)=b/(c+2a)=c/(a+2b),且a+b+c≠0,求(3b+c)/b的值?

已知a/(b+2c)=b/(c+2a)=c/(a+2b),且a+b+c≠0,求(3b+c)/b的值?
已知a/(b+2c)=b/(c+2a)=c/(a+2b),且a+b+c≠0,求(3b+c)/b的值?

已知a/(b+2c)=b/(c+2a)=c/(a+2b),且a+b+c≠0,求(3b+c)/b的值?

a/(b+2c)=b/(c+2a)=c/(a+2b)
∵a+b+c≠0
根据等比定理
a/(b+2c)=b/(c+2a)=c/(a+2b)=(a+b+c)/(b+2c+c+2a+a+2b)=1/3
∴b+2c=3a,c+2a=3b,a+2b=3c
∴b+2c=3a=3(3c-2b)=9c-6b
7b=7c
b=c
(3b+c)/b
=(3b+b)/b
=4b/b
=4