设x,y为实数,若若4x²+y²+xy=1,则2x+y的最大值是

设x,y为实数,若若4x²+y²+xy=1,则2x+y的最大值是
设x,y为实数,若若4x²+y²+xy=1,则2x+y的最大值是

设x,y为实数,若若4x²+y²+xy=1,则2x+y的最大值是
2x+y的最大值是:2√10/5．

4x^2+y^2 + xy = 1 => 4x^2+y^2 = 1 - xy, (2x+y)^2 = 1 + 3xy
4x^2+y^2 ≥ 2*2x*y = 4xy, 1-xy ≥4xy => xy ≤ 1/5
(2x+y)^2 = 1 + 3xy ≤ 1+ 3/5 = 8/5
2x+y ≤ √(8/5)
2x+y的最大值 √(8/5)