Question

不等式求证:a/根号b+b/根号c+c/根号a大于等于根号a+根号b+根号c

Answer 1

a/√b+√b>=2√(a/√b*√b)=2√a

b/√c+√c>=2√(b/√c*√c)=2√b

c/√a+√a>=2√(c/√a*√a)=2√c

相加

a/√b+b/√c+c/√a+√a+√b+√c>=2√(a+2√b+2√c

所以

a/√b+b/√c+c/√a>=√a+√b+√c