1÷a+1÷b+1÷c大于等于1÷根号下ab+1÷根号下bc+1÷根号下ac

1÷a+1÷b+1÷c大于等于1÷根号下ab+1÷根号下bc+1÷根号下ac
1÷a+1÷b+1÷c大于等于1÷根号下ab+1÷根号下bc+1÷根号下ac

1÷a+1÷b+1÷c大于等于1÷根号下ab+1÷根号下bc+1÷根号下ac
1÷a+1÷b+1÷c=(1/2)[(1/a+1/b)+(1/a+1/c)+(1/b+1/c)]
≥(1/2)[2√(1/a)(1/b)+2√(1/a)(1/c)+2√(1/b)(1/c)]
=1/√(ab)+1/√(ac)+1/√(bc)
得证