Let x > 0, Y > 0, and (x-1) (Y-1) ≥ 2, then the value range of XY is?

Let x > 0, Y > 0, and (x-1) (Y-1) ≥ 2, then the value range of XY is?

(x-1)(y-1)≥2
xy-(x+y)+1≥2
xy≥1+x+y 1)
xy≥1+√(x^2+y^2+2xy)
xy-1≥√(x^2+y^2+2xy)
(xy)^2-2xy+1≥x^2+y^2+2xy>=4xy
(xy)^2-6xy+1≥0
XY ≥ 3 + 2 √ 2 or XY ≤ 3-2 √ 2
From 1), XY > 1
So XY ≥ 3 + 2 √ 2

High school mathematics problems (basic inequalities) Given a > 0, find the minimum value of the function y = (x? + A + 1) / (x? + a) ^ 1 / 2

If + M = (M 2) / M 2 = m 2 / 2, then it is equal to (M 2) / M 2
If and only if M = 1, that is, x 2 + a = 1, the equal sign is taken

1. Let a and B be the solution sets of inequality 3x ^ 2 + 60 respectively. Try to find a intersection B and a union B 2. It is known that the solution set of inequality ax ^ 2-3x + 6 > 4 is {x | XB} (1) Find a, B (2) Solve the inequality ax ^ 2 - (AC + b) x + BC1 / 4 2、 Fill in the blanks 1. If the inequality of X is x ^ 2-ax-a

Let me answer you, one, one. Solve 3x ^ 2 + 6

A high school mathematics problem (basic inequality) Given that x.y.z > 0 and X + 3Y + 4Z = 6, find the maximum value of x ^ 2Y ^ 3Z

There are 6 = x / 2 + X / 2 + y + y + y + y + 4Z + 4Z ≥ 3 (x / 2 * x / 2 * 2 * y * y + y + y + 4Z + 4Z ≥ 3 (x / 2 * x / 2 * 2 * y) ^ {1 / 3} + 3 (y * y * 4 * 4Z) ^ (1 / 3) (ternary mean) ≥ 2 [3 (x / 2 * x / 2 * 2 * y) ^ {1 / 3} * 3 (y * y * 4Z) ^ (1 / 3)] ^ {1 / 2} (binary mean) = 6 (x ^ 2Y ^ 3Z) ^ {1 / 6} therefore (x ^ 2Y ^ 2Y ^ 3Z ^ 1 / 6} therefore (x ^ 2Y ^ 2Y ^ ^ 3Z) ^ {1 / 6}

α β γ is a triangle with three internal angles Confirmation: sin α + sin β + sin γ

(1) Let f (x) = SiNx x x belong to (0, Π) be concave functions and have Jensen inequality (f (x) + F (y) + F (z)) / 3

(only determinants, only determinants! Determinants! Only determinants!) 1. The price of type a refrigerator is 2190 yuan, and the daily electricity consumption is 1 kilowatt. Although the price of type B energy-saving refrigerator is 10% higher than that of type a refrigerator, the daily power consumption is only 0.55 degree. Now, the A-type refrigerator is sold at a discount (the price after 10% discount is 1 / 10 of the original price). It is only worthwhile for consumers to buy at least a few discounts in the shopping mall (the price is 0.40 yuan per kilowatt hour for 365 days per year with a service life of 10 years)? 2. A taxi starts at 10 yuan (driving within 5km needs to pay 10 yuan). When it reaches or exceeds 5km, the fare will be increased by 1.2 yuan (less than 1km). If someone takes a taxi from place a to place B, he will pay 17.2 yuan. What is the distance from place a to place B?

1 2190x1.1+365x10x0.55x0.4>2190x y+365x10x1x0.4 y=?

Now we want to produce 20 pieces of product a and B. product a needs 15kg raw material a and 20kg raw material B; product B needs 20kg raw material a and 10kg raw material B. now raw material a has 360kg and raw material B is 300kg. It is known that the cost of producing product a is 10 yuan per piece and that of product B is 8 yuan (1) What are the production plans that meet the requirements? Please state the reasons (2) How many pieces of product a can make the production cost lowest? Why?

(1) Suppose x pieces of a product and (20-x) pieces of product B are produced. According to the meaning of the question, 15x + 20 (20 − x) ≤ 360, ① 20x + 10 (20 − x) ≤ 300 ②, by solving inequality ①, X ≥ 8, by solving inequality ②, X ≤ 10. Therefore, the solution set of inequality group is 8 ≤ x ≤ 10. Therefore, the production scheme in line with the requirements is

Some practical mathematical inequalities 1. Let a and B be positive numbers and compare the size of a ^ 3-B ^ 3 and 3a ^ 2 (a-b) 2. There are four continuous integers whose product is greater than 120. Try to find the minimum four continuous natural numbers to meet this requirement 3. Erase a number from 1,2,3,4,..., a group of continuous positive integers on the blackboard. The average value of the remaining numbers is 602 / 17?

1.(a^3-b^3)-(3a^2(a-b))=(a-b)(a^2+ab+b^2)-3a^2(a-b)
=(a-b)(ab+b^2-2a^2)
=-(a-b)^2(2a+b)

In the activity of protecting the earth and cherishing the homeland, the Youth League Committee of the school assigned a batch of saplings to the students of class 1 of grade 9 to plant. If each student was divided into two trees, there were 42 seedlings left; if each person in front of each person was divided into three trees, the last one got less than five seedlings (but only one less) (1) If there are X students in class 1 of grade 9, how many seedlings are there (2) At least how many students are there in class 1 of grade 9? How many students are there at most?

There are X students in class 1 of grade 3, and the total number of saplings is 2x + 42
And 1 ≤ [2x + 42] - 3 (x-1) < 5
There are at least 41 and at most 44 people solving inequality 40
I think there is an implied condition x > 42, or it will be distributed to everyone
At least 43, up to 44

On practical problems of mathematical inequality A has 1530 goods, B has 1150, arrange the freight car to Guangzhou, the freight car can hang two kinds of containers a, B 50, known a = a 35 + B 15, B = a 25 + B 35, to arrange the number of containers, what are the transport options?

Let X be a kind of container, then B kind of container is (50-x), then the inequality is: 35x + 25 (50-x) ≥ 153015x + 35 (50-x) ≥ 11500 ≤ x ≤ 50x ∈ n + to solve the above inequality, we can get 28 ≤ x ≤ 30, so x = 28 x = 29 x = 30. The first scheme is 28 containers of type A and 22 sections of containers of type B. the second scheme is 29 sections of containers of type A