√(xy)≤(a-1)x+2ayxy≤(a-1)^2x^2+4a^2y^2+4a(a-1)xy(a-1)^2x^2+4a^2y^2+[4a(a-1)-1]xy≥04a^2(y/x)^2+(4a^2-4a-1)(y/x)+ (a-1)^2 ≥0若上式恒成立需满足:(-4a^2+4a+1)/(8a^2)≤0解得a≥(1+√2)/2故a的最小值为(1+√2)/2。
