Question

已知实数a,b,c,满足a+b+c=10,且1/(a+b)+1/(b+c)+1/(b+c)=14/17,求a/(b+c)

Answer 1

a/(b+c)+b/(a+c)+c/(a+b)

=[10-(b+c)]/(b+c)+[10-(a+c)]/(a+c)+[10-(a+b)]/(a+b)

=10/(b+c)-1+10/(a+c)-1+10/(a+b)-1

=10[1/(a+b)+1/(b+c)+1/(b+c)]-3

=140/17-3

=89/17