设x,y是实数.若4x^2+y^2+xy=1,则2x+y的最大值

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)