已知abc均为正实数,求证b²/a＋c²/b＋a²/c≥c√b/a＋a√c/b＋b√a/c

已知abc均为正实数,求证b²/a＋c²/b＋a²/c≥c√b/a＋a√c/b＋b√a/c
已知abc均为正实数,求证b²/a＋c²/b＋a²/c≥c√b/a＋a√c/b＋b√a/c

已知abc均为正实数,求证b²/a＋c²/b＋a²/c≥c√b/a＋a√c/b＋b√a/c
2（b²/a＋c²/b＋a²/c）=(b^2/a+a^2/c)+(c^2/b+b²/a)+（a^2/c+c^2/b)>=2
√(b^2/a)*(a^2/c)+2√(c^2/b)*(b²/a)+2√(a^2/c)*(c^2/b)=2(b√a/c+c√b/a+a√c/b),即b²/a＋c²/b＋a²/c≥c√b/a＋a√c/b＋b√a/c.