已知a,b是正实数,用比较法证明根号b分之a加根号a分之b大于等于根号a加根号b

Question

已知a,b是正实数,用比较法证明根号b分之a加根号a分之b大于等于根号a加根号b

Answer 1

设x=√a,y=√b
x^2-xy+y^2≥xy
(x+y)*(x^2-xy+y^2)≥xy(x+y)
x^3+y^3≥xy(x+y)
(x^3+y^3)/(xy)≥(x+y)
(x^2/y+y^2/x)≥(x+y)
(a/√b+b/√)≥(√a+√b)
毕!