已知:x=a/b+c,y=b/a+c,z=c/a+b.求证:x/1+x + y/1+y + z/1+z=1
问题描述:
已知:x=a/b+c,y=b/a+c,z=c/a+b.求证:x/1+x + y/1+y + z/1+z=1
其中“/” 为分数线
答
因为x+1=(a+b+c)/(b+c),则1/(x+1)=(b+c)/(a+b+c)y+1=(a+b+c)/(a+c),则1/(y+1)=(a+c)/(a+b+c)z+1=(a+b+c)/(a+b),则1/(z+1)=(a+b)/(a+b+c)则x/(1+x) + y/(1+y) + z/(1+z)=3-1/(x+1)-1/(y+1)-1/(z+1)=3-(2a+2b+2c)/(a...