Question

不等式选讲题目已知a b为正实数,求证b分之a的平方＋a分之b的平方≥a＋b

Answer 1

a^2/b+b^2/a = (a^3+b^3)/ab = (a+b)(a^2+b^2-ab)/ab >= (a+b)(2ab-ab)/ab = a+b

中间用到了均值不等式a^2+b^2>=2a