已知xy/(x+y)=a,xz/(x+z)=b,yz/(y+z)=c,且a.b.c不等于0,求x的值

题目

已知xy/(x+y)=a,xz/(x+z)=b,yz/(y+z)=c,且a.b.c不等于0,求x的值

答案

a≠0,xy≠0 x≠0且y≠0；同理,b≠0,x≠0,z≠0综上,得x,y,z≠0xy/(x+y)=a(x+y)/(xy)=1/a1/x+1/y=1/a (1)同理1/x+1/z=1/b (2)1/y+1/z=1/c (3)[(1)+(2)+(3)]/21/x+1/y+1/z=(1/a+1/b+1/c)/2 (4)(4)-(3)1/x=(1/a+1/b+1/c)...