ab/a+b=2,ac/a+c=5,bc/b+c=求 a +b+c的值
1个回答

c/b+c=?,你题目漏抄了吧.我就用?代替那数.

显然,a,b,c均不为0

ab/a+b=x,显然b≠x,∴a=xb/(b-x).

ac/a+c=y,显然a≠y,∴c=ya/(a-y).将a代入得c=xyb/[xy+(x-y)b]

bc/b+c=z,显然b≠z,∴c=zb/(b-z),代入得xyb/[xy+(x-y)b]=zb/(b-z)

∴b=2xyz/(xy+yz-xz)=20?/(10+5?-2?)

由于对称性,a=2xyz/(xy+xz-yz)=20?/(10+2?-5?)

c=2xyz/(xz+yz-xy)=20?/(2?+5?-10)

a+b+c=20?/(10+5?-2?)+20?/(10+2?-5?)+20?/(2?+5?-10)