If x is greater than zero, y is greater than zero, 2x + y = 1, then the minimum value of 1 / x + 1 / y is 0

If x is greater than zero, y is greater than zero, 2x + y = 1, then the minimum value of 1 / x + 1 / y is 0

If 2 / X and 4 / y = 1, find the minimum value of X + y

x+y=(2/x+4/y)*(x+y)
=6+2*y/x+4*x/y
>=6+4*sqrt(2)

X + y = 1 / 2 find the minimum value of 1 / x + 4 / Y
1/x+4/y>=2√(1/x*4/y)
Take the equal sign if and only if 1 / x = 4 / y
Because x + y = 1 / 2
The solution of simultaneous equations is x = 1 / 10, y = 2 / 5
I.e. 1 / x = 10 4 / y = 10
So 1 / x + 4 / Y > = 2 √ (1 / X * 4 / y) = 2 √ (10 * 10) = 20
Why is this not right?
The correct answer is 18

Let x = 2 cos θ y = 1 sin θ x y = 3 sin θ cos θ = 3 radical 2Sin (θ π / 4), so the maximum value is 3 radical 2 and the minimum value is 3 radical 22) y / x = y-0 / x-0 is the point to point on the circle