本帖最后由 hbghlyj 于 2020-4-7 18:48 编辑
下面是否正确?
(1)$a,b,c>0,a + b + c = 1 ,\sqrt a+ \sqrt b+ \sqrt c= \sqrt2$,则$\sum\frac{a}{\sqrt b +\sqrt c}\le\frac75\sqrt2$,取等当且仅当$\left(\frac89,\frac1{18},\frac1{18}\right)$
(2)$a,b,c,d>0,a + b + c + d = 1,\sqrt a+\sqrt b+\sqrt c+\sqrt d=\frac13(2\sqrt{3}+\sqrt6),$则$\sum\frac a{\sqrt2-\sqrt a}$当$\left(\frac1{12} (6 - 2\sqrt2 - \sqrt3),\frac1{12} (6 - 2\sqrt2 - \sqrt3),\frac1{12} (6 - 2\sqrt2 - \sqrt3),\frac1{36} (6 + 2\sqrt2 + \sqrt3)\right)$时取最大值,当$\left(\frac1{12} (6 - 2\sqrt2 + \sqrt3),\frac1{12} (6 - 2\sqrt2 + \sqrt3),\frac1{12} (6 - 2\sqrt2 +\sqrt3),\frac1{36} (6 + 2\sqrt2 - \sqrt3)\right)$时取最小值 |