已知实数abc满足a+b+c=10 1/(a+b)+1/(b+c)+1/(a+c)=14/17 求a/(b+c)+b/(a+c)+c/(a+b)的值
问题描述:
已知实数abc满足a+b+c=10 1/(a+b)+1/(b+c)+1/(a+c)=14/17 求a/(b+c)+b/(a+c)+c/(a+b)的值
答
a+b+c=10
a=10 - (b+c)
b=10 -(a+c)
c=10 -(a+b)
原式 =10/(b+c)-1+10/(a+c)-1+10/(a+b)-1
= 10(1/(a+b)+1/(b+c)+1/(a+c))-3
= 140/17 -3
= 89/17