Question

若 a b x y属于正实数 且a/x+b/y=1 证明x+y>=根号下a+根号下b的平方

Answer 1

x+y=(x+y)*1

=(x+y)*(a/x+b/y)

=a+b+(ay/x+bx/y)

≥a+b+2√(ay/x*bx/y)

=a+b+2√(ab)

=(√a+√b)^2