设x,y为实数且3≤xy^2≤8,4≤x^2/y≤9,则x∧3/y^4的最大值

Question

设x,y为实数且3≤xy^2≤8,4≤x^2/y≤9,则x∧3/y^4的最大值

Answer 1

令XY^2=a,x^2/y=b
x^3/y^4=b^2/a
由已知得
1/8 ≤1/a≤1/3
16≤b^2≤81
∵1/a＞0,b^2＞0
∴﹙1/8﹚*16≤b^2/a≤﹙1/3﹚*81
即2≤ x^3/y^4≤27