a＞b＞c求证1/(a-b)+1/(b-c)≥4/(a-c)怎么做.在下才疏学浅请各位兄台多多帮忙.谢谢

Question

a＞b＞c求证1/(a-b)+1/(b-c)≥4/(a-c)怎么做.在下才疏学浅请各位兄台多多帮忙.谢谢

Answer 1

左边1/(a-b)+1/(b-c)≥2*根号下1/{(A-B)(B-C)} 右边,A-C=A-B+B-C≥2*根号下{(A-B)(B-C)},那么4/(a-c)小于等于2*根号下1/{(A-B)(B-C)},所以1/(a-b)+1/(b-c)≥4/(a-c)