(2x) 2+y 2 is greater than or equal to 4xy.

So 5xy is less than or equal to 1.

Xy ≤ 1/5

(2x+y)^2=4x^2+y^2+xy+3xy= 1+3xy

So 1+3xy is less than or equal to 1+3/5=8/5.

That is, (2x+y) 2 is less than or equal to 8/5.

So 2x+y is greater than or equal to (-2 root number 10)/5 and less than or equal to (2 root number 10)/5.

So the maximum value of 2x+y is (2 root numbers 10)/5.

The answer upstairs is liberal arts.