2x^2-axy+y^2<=0对任意x∈[1,2],y∈[1,3]恒成立,
<==>a>=2x/y+y/x①对任意x∈[1,2],y∈[1,3]恒成立,
设t=x/y,x∈[1,2],y∈[1,3],则t∈[1/3,2],
①变为a>=2t+1/t,记为f(t),
t=1/√2时f(t)取最小值,
f(1/3)=11/3,f(2)=9/2,为最大值,
∴a>=9/2,为所求.