For positive numbers x, y, if x + 2Y + xy = 30, then the value range of XY is

For positive numbers x, y, if x + 2Y + xy = 30, then the value range of XY is

x+xy=30-2y
x=(30-2y)/(1+y)
xy=(30y-2y^2)/(1+y)
Let 1 + y = t, y = T-1
xy=[30(t-1)-2(t-1)^2]/t
=(-2t^2+34t-32)/t
=34-2(t+16/t)
Because X / y is a positive number, 1

Given x > 0, Y > 0, lgx + lgY = 2, find 5x + 2Y

lgxy=2
xy=100
x>0,y>0
5x+2y>=2√(5x*2y)=20√10
So the minimum value of 5x + 2Y is 20 √ 10

x. Y ∈ R + and lgx + lgY = 1, find the minimum value of X + 2Y

∵lgx+lgy=lg（xy）=1,
∴xy=10
x+2y≥2√（x*2y）=2√20=4√5（x,y＞0）
The minimum value of X + 2Y is 4 √ 5

If lgx + lgY = 1, then the minimum value of 2 / x + 5 / y is?
fast
How to seek,

lgx+lgy = 1 => lgx = 1- lgy => x = 10^(1-lgy) => x = 10/y
2 / x + 5 / y = Y / 5 + 5 / y = = > y tends to 5, = 2 minimum