Let X and y be positive real numbers, 2x + 3Y = 3, then the minimum value of 3x + 5Y is______ ．

Let X and y be positive real numbers, 2x + 3Y = 3, then the minimum value of 3x + 5Y is______ ．

∵ x, y are positive real numbers, 2x + 3Y = 3, ∵ 3x + 5Y = 13 (2x + 3Y) (3x + 5Y) = 13 (21 + 9yx + 10xy) ≥ 13 (21 + 29yx · 10xy) = 7 + 610, if and only if x = 10 − 22, y = 5 − 103, take the equal sign. So the answer is 7 + 610

If real numbers, x, y satisfy x2 + y2-2x-6y + 9 = 0, find the maximum value of (1) y / x, and the value range of (2) (Y-2) / (x + 2)
(3) The value range of x2 + Y2
(4) The second power of (x + 2) + the second power of (Y-2)

(x-1) ^ 2 + (Y-3) ^ 2 = 1, the trajectory is a circle with (1,3) as the center and 1 as the radius, (1) y / X is the slope of the line between a point on the circle and the origin, the graph shows that Y / X is greater than or equal to 4 / 3 (2) (Y-2) / (x + 2) is the slope of the line between a point on the circle and (- 2,2), the graph shows that (Y-2) / (x + 2) is greater than or equal to 0, less than or

If the real number a is known such that at least one of the three univariate quadratic equations, x2-x + a = 0, x2-2x + a = 0, x2-4x + a = 0, has a solution, the value range of a is obtained

If the equation has real roots, the discriminant delta > = 0
At least one of the three equations has roots (take the union of a)
So 1-4a > = 0 or 4-4a > = 0 or 16-4a > = 0
So a