Simple calculation, known x = 11 / 75, y = 25 / 22, find the value of (x = y) ^ 2 - (X-Y) ^ 2

Simple calculation, known x = 11 / 75, y = 25 / 22, find the value of (x = y) ^ 2 - (X-Y) ^ 2

(x+y)^2-(x-y)^2
=(x+y+x-y)(x+y-x+y)
=2x*2y
=4xy
=4×11/75×25/22
=2/3

Given x ^ 2 + y ^ 2 = 25, x + y = 7, find the value of (X-Y) ^ 2 and tell me how to calculate 2XY

∵X+y=7,
∴（X+y）²=7²
∴x^2+2xy+y^2=49
∵x^2+y^2=25
∴2xy=49-25=24
（x-y)^2=x^2-2xy+y^2=25-24=1

Calculation: 1, - two thirds √ 81 2, (√ x + y) & # 178; - (√ X-Y) & # 178;

1. - two thirds √ 81 = - 2 / 3 x9 = - 6
2、（√x+y）²-（√x-y）²=x+y-（x-y）=x+y-x+y=2y

The fast and slow trains leave from a and B at the same time. After 5 hours, the two trains meet at 50 kilometers from the midpoint. It is known that the fast train travels 75 kilometers per hour
How many kilometers per hour does the local train travel? (solved by equation)

The fast and slow trains leave from a and B at the same time. After 5 hours, the two trains meet at a distance of 50 kilometers from the midpoint. It is known that the fast train travels 75 kilometers per hour and the slow train travels how many kilometers per hour? (use equation solution)
Let the idle speed be x km
(75-x)*5==50*2
375-5x==100
5x==275
x==55
A: the speed of the local train is 55 km / h

In trapezoidal ABCD, ab ∥ CD, a = 60 °, B = 30 ° and ad = CD = 6, then the length of AB is ()
A. 9B. 12C. 18D. 6+33

Through point C, make CE ∥ ad, intersect AB at point E, ∥ ab ∥ CD, CE ∥ ad, ad = CD = 6, ∥ quadrilateral AECD is rhombus, ∥ AE = CE = ad = 6; from CE ∥ ad, ∥ CEB = ∥ a = 60 °; in △ ECB, ∥ CEB = 60 °, ∥ B = 30 °, ∥ ECB = 90 ° according to "the angle of 30 ° in a right triangle, the right side opposite is oblique

A pile of coal weighs four fifths of a ton. One twentieth of it is used. How much is left

4 / 5x (1-1 / 20) = 4 / 5x19 / 20 = 19 / 25 tons, there are still 19 / 25 tons left

Mean inequality one positive two definite three phases and so on what meaning? Why should we emphasize this?

A + b > = 2 * radical (AB)
A, b > 0
Binary: the product of a and B is a definite value
Three phase: that is to say, after using this inequality, we must verify whether "=" is true
The method is to see if a + B equals 2 * radical (AB) when a = B

The two passenger and freight trains leave for Party A and Party B at the same time. After 5 hours, they meet. The distance between the two places is 770 km. It is known that the speed of the passenger train is 1.2 times that of the freight train

X*5+1.2*X*5=770
11X=770
X=70
1.2*X=84
So the passenger car is 84km / h and the freight car is 70km / h

The basic inequality of the first grade of senior high school
Seventeen freight trains with a batch of goods drive from city a to city B at a constant speed of V km / h. It is known that the length of the two railway lines is 400 km, and the distance between each freight train has to be less than (V / 20) square kilometers. It will take several hours to transport this batch of goods to city B at the earliest

17 freight cars are regarded as a train with length L = 16 * (V / 20) square meters
When all of them arrive, they are actually equivalent to a train with a speed of V and a distance of (400 + L)
t=（400+L）/v=(400+16*(v/20)*(v/20))/v=(400/v)+16v/400
According to the inequality, the minimum time is
T = 2 times root (400 / V) * (16V / 400) = 8

Party A and Party B get together 595 kilometers, a bus and a truck leave from Party A and Party B at the same time, and meet after 3.5 hours
The ratio of passenger cars to speed is 9:8. How many kilometers do passenger cars and freight cars travel per hour?

If the passenger car runs 9A km per hour, the freight car runs 8A km
3.5(9a+8a)=595
59.5a=595
a=10
It is 90 km / h for passenger cars and 80 km / h for freight cars