Question

证1/a+1/b+1/c≥2/(a+b)+2/(b+c)+2/(a+c)

Answer 1

1/a+1/b=a+b/ab≥4(a+b)/(a+b)^2=4/a+b

同理.

1/a+1/c=a+c/ac≥4(a+c)/(a+c)^2=4/a+c

1/c+1/b=c+b/cb≥4(c+b)/(c+b)^2=4/c+b

相加

2(1/a+1/b+1/c)≥4/(a+b)+4/(b+c)+4/(a+c)

所以

1/a+1/b+1/c≥2/(a+b)+2/(b+c)+2/(a+c)