Question

已知a,b是正实数,求证:(a/根号b)+(b/根号a)>=(根号a)+(根号b)

Answer 1

a/√b+b/√a

=(a√a+b√b)/(√a*√b)

=[(√a)^3+(√b)^3]/√(ab)

=(√a+√b)(a-√a√b+b)/√(ab)

>=(√a+√b)(2√a√b-√a√b)/√(ab) (a+b>=2√a√b)

=(√a+√b)(√a√b)/√(ab)

=√a+√b

证毕