Question

已知A／X=BC／B+C,B／Y=CA／C+A,Z／C=AB／A+B,试求1／X+1 + 1／Y+1 + 1／Z+1的值

Answer 1

x/A=(B+C)/BC=1/C+1/B

X/A+1/A=(X+1)/A=1/C+1/B+1/A

1/(X+1)=1/[A(1/A+1/B+1/C)]

Y/B=1/C+1/A

(Y+1)/B=1/C+1/A+1/B

Z/C=1/A+1/B

(Z+1)/C=1/A+1/B+1/C

1/(X+1)+1/(Y+1)+1/(Z+1)=1/[A(1/A+1/B+1/C)]+1/[B(1/A+1/B+1/C)]+1/[C(1/A+1/B+1/C)]

=(BC+AC+AB)/[ABC(1/A+1/B+1/C)]

=(BC+AC+AB)/(BC+AC+AB)

=1