已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c

问题描述:

已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c

设a+b=2t (1)b+c=3t (2)a+c=7t (3)三个等式相加得:2a+2b+2c=12t两边除以2得:a+b+c=6t (4)(4)-(1) 得:c=4t(4)-(2)得:a=3t(4)-(3)得:b=-t ∴1/a:1/b:1/c=1/(3t):1/(-t):1/(4t)=4:...