Several high school two inequality math problems / urgent! 1. Given 3A ^ 2 + 2B ^ 2 = 5, find the maximum value of y = (2a ^ 2 + 1) (b ^ 2 + 2)? A ^ 2 means the square of A 2. A city uses 37 vehicles to transport a batch of relief materials to the disaster area. Assuming that the speed is v km / h, the route is known to be 400 km long. For safety, the distance between two vehicles should not be less than (V / 20) square kilometers. Then, what is the shortest time for all these materials to reach the disaster area? 3. Let a + B = 1, a > = 0, b > = 0, then the maximum value of a ^ 2 + B ^ 2? A ^ 2 means the square of A 4. Let x > 0, Y > 0, M = (x + y) / (2 + X + y), n = {X / (2 + x)} + {Y / (2 + y)}, then the size relation of M and N? If not, you can only answer yes!

Several high school two inequality math problems / urgent! 1. Given 3A ^ 2 + 2B ^ 2 = 5, find the maximum value of y = (2a ^ 2 + 1) (b ^ 2 + 2)? A ^ 2 means the square of A 2. A city uses 37 vehicles to transport a batch of relief materials to the disaster area. Assuming that the speed is v km / h, the route is known to be 400 km long. For safety, the distance between two vehicles should not be less than (V / 20) square kilometers. Then, what is the shortest time for all these materials to reach the disaster area? 3. Let a + B = 1, a > = 0, b > = 0, then the maximum value of a ^ 2 + B ^ 2? A ^ 2 means the square of A 4. Let x > 0, Y > 0, M = (x + y) / (2 + X + y), n = {X / (2 + x)} + {Y / (2 + y)}, then the size relation of M and N? If not, you can only answer yes!

1, (2a ^ 2 + 1) (b ^ 2 + 2) less than or equal to ((2a ^ 2 + 1 + B ^ 2 + 2) / 2) ^ 2
If and only if 2A ^ 2 + 1 = B ^ 2 + 2, the equal sign holds
Substituting 3A ^ 2 + 2B ^ 2 = 5, a = positive and negative 1, B = positive and negative 1
So the maximum is 9
2. We can know that the actual distance is equal to the distance from the first car to the last car plus the original distance, and the distance between 37 cars is 36 segments
Then the minimum actual distance = ((V / 20) ^ 2) * 36 + 400
Minimum actual time = ((V / 20) ^ 2) * 36 + 400) / v = 0.09v + 400 / V
Less than or equal to 2 * radical (0.09v * 400 / V) = 12 if and only if
When 0.09v = 400 / V, i.e. v = 200 / 3, it takes 12 hours for the equal sign to be established
3, let a = (Sina) ^ 2, B = (COSA) ^ 2
a^2+b^2=(sinA)^4+(cosA)^4=(1-(cosA)^2)^2+(cosA)^4
=2 (COSA) ^ 4-2 (COSA) ^ 2 + 1 let (COSA) ^ 2 = t
0 less than or equal to t less than or equal to 1 is converted into a quadratic function
The maximum solution is 1
4,M=1-2/(2+x+y),N=2-2/(2+x)-2/(2+y)
From N-M = 1-2 / (2 + x) - 2 / (2 + y) + 2 / (2 + X + y), the,
=1-2((4+x+y)/(xy+2x+2y+4)-1/(2+x+y))
>1-2((4+x+y)/(2x+2y+4)-1/(2+x+y))
=1-2((4+x+y)/(2x+2y+4)-2/(4+2x+2y))
=1-2*1/2=0
So n > m

According to the statistics of a sample survey of households in a township, the total annual average consumption expenditure of households in 2003 was 10000 yuan, including food consumption
It is predicted that after 2003, the average total consumption expenditure of each household will increase by 3000 yuan per year
In 2005, the living conditions of the people in this town can reach the well-off level (that is, the Engel coefficient n meets the condition of 40% < n)

Average consumption expenditure of each household in 2005 = 10000 + 3000 + 3000 = 16000
Suppose that the average annual growth rate of food consumption per household in this township is X
Average food consumption per household in 2005 = 6000 (1 + x) (1 + x)
It is estimated that the Engel coefficient will be 6000 (1 + x) (1 + x) / 16000 in 2005
Make 40% < 6000 (1 + x) (1 + x) / 16000 ≤ 50%
3.28＜x≤15.47%