4x^2+y^2 + xy = 1 => 4x^2+y^2 = 1 - xy, (2x+y)^2 = 1 + 3xy4x^2+y^2 ≥ 2*2x*y = 4xy, 1-xy ≥4xy => xy ≤ 1/5(2x+y)^2 = 1 + 3xy ≤ 1+ 3/5 = 8/52x+y ≤ √(8/5)2x+y的最大值 √(8/5)
2x+y的最大值是: 2√10/5．
