Question

初二数学题：1.若X=a/(b+c)=b/(a+C)=C/(a+b)，求X的值。2.已知a/b=(a-c)/(c-b),求证1/a+1/b=2/c,谢谢

Answer 1

1, X=a/(b+c)=b/(a+C)=C/(a+b)=(a+b+c)/(2a+2b+2c)=1/2
2, a/b=(a-c)/(c-b)= (2a-c)/c= c/(2b-c)
2ab=ab+bc
1/a+1/b=2/c

错了，第一道题还少了a+b+c=0的情况，所以当a+b+c=0时X=a/-a=-1

Answer 2

1, X=a/(b+c)=b/(a+C)=C/(a+b)=(a+b+c)/(2a+2b+2c)=1/2
2, a/b=(a-c)/(c-b)= (2a-c)/c= c/(2b-c)
2ab=ab+bc
1/a+1/b=2/c

都是分式定理，若a/b=c/d，则(a-c)/(b-d)=(a+c)/(b+d)=a/b=c/d

Answer 3

X=a/(b+c)=b/(a+C)=C/(a+b)=A+B+C/b+c+a+C+a+b=A+B+C/2A+2B+2C=1/2
(2)a/b=(a-c)/(c-b)交叉相乘得ac-ab=ab-bc
∴c(a+b)=2ab
∴还原得a+b/ab=2/c
∵a+b/ab=1/a+1/b
∴1/a+1/b=2/c