A math problem, urgent, ask for a detailed solution

<> dear, if you are satisfied with the answer, let's do it!! Thank you.

It's not good to write up, so I'll give you ideas.

Divide both sides of the equation by y, it becomes an equation with x y, look at x y as a whole, solve x y equals 4 and look at the problem, divide the numerator and denominator of the problem by y, then it becomes a fraction with x y, and then bring x y=4 in, and we get 6 5

x cannot be equal to y, if x=y=0 is not in line with the topic.

Solution: x- xy-2y=0

x-2y= xy 0 x 2y

x^2-4xy+4y^2=xy

x-4y）（x-y）=0

x=4y x=y (rounded).

x=4y substitution gets:

Because x 0, y 0

Molecule = 8y-2y = 6y

Denominator = y + 4y = 5y

So it is reduced to 6 5.

Factoring the equation into ( x-2 y)( x+ y)=0 solves x=2 y or x=- y

Substituting it into the equation results in 6 5 or 1 3

x-root number xy-2y=0

x-2y = root number xy

x-2y)^2=xy

x^2-5xy+4y^2=0

Multiply with crosses.

x-y)(x-4y)=0

x-y=0 or x-4y=0

x=y or x=4y

When x=y.

Original = 1 3

When x=4y.

Original = 6 5

Let the area of the larger square be x1 and the smaller one be x2, there is x1+x2=468, x1-x2=180, so x1=324, x2=64, so the side length is 18,8

So one is 18

So the other one is 12

If the two squares have side lengths a and b respectively, there is.

a^2+b^2=468

a^2-b^2=180

The above two equations are obtained.

a=18，b=12

The big 18 and the small 12 let the side length of the large square be x, and the side length of the small square is y, x*x+y*y=468

x*x-y*y=180

The solution is x=18 and y=12

Solution: y=f(x)=(2x+5) (x-3)=[2x-6)+11] (x-3)=2+11 (x-3), and the forest collapses x=11 (y-2)+3, i.e., f -1(x)=11 (x-2)+3

Then f -1 (x+1) = 11 (x-1)+3 gives x=11 (y-3)+1, that is, y=g(x)=11 split key (x-3)+1

g(4)=11 This circle(4-3)+1=11+1=12

丨a+b丨-丨a+c丨-丨b-a丨-丨b-c丨.

a-b+a+c-b-a-c+b

a-b

Let z = -1 (2 x). Because -3 x 2 and z is a monotonically increasing function of x, -8 z -1 4.

Then the original formula can be reduced to g(z) = f(x)=z 2+z+1, because a 0, so g(z) opens upward, and the minimum abscissa z=-1 2 is in -8 z -1 4, so the minimum value of g(z) is g(-1 2)=3 4, and the maximum value is g(-8)=57

Therefore, the maximum and minimum of f(x) can also be obtained.

A 1 hour 1 15, B 1 hour 1 12.

4 (1 15 + 1 12) = 5 hours.

Solution :(1) The random variables x and y are independently and identically distributed.

The possible values of u are 1 and 2;The possible value of v is 1,2p(u=1;v=1）=p(x=1；y=1)=p（x=1）*p（y=1）=2/3*2/3=4/9

p（u=1；v=2）=0

p（u=2；v=1）=p（x=2；y=1）+p(x=1；y=2)=1/3*2/3+1/3*2/3=2/9+2/9=4/9

p（u=2；v=2）=p（x=2；y=2)=1 3*1 3=1 9 and then draw the probability distribution of (u,v), here I omit ah (2) Do you want to ask cov(u,v)

eu=1*4/9+2*5/9=14/9

ev=1*8/9+2*1/9=10/9

EUV = 1 * 4 9 + 2 * 4 9 + 4 * 1 9 = 16 9 (UV distribution omitted) CoV (u, v) = EUV--- EUEV = 16 9---14 9 * 10 9 = 4 81

If you don't understand, ask me again.

The angle PBC is 60°, PB=PC=root number 2, SO triangle PBC is the equilateral triangle to find the height of the triangle PBC, the pyramid A-PBC, through the A perpendicular line, the intersection of the bottom surface is higher than a point D, the D point divides the height into two parts, the ratio is 1:2, find the PD, and then use the Pythagorean to find AD, AD is the height of the pyramid, the bottom equilateral triangle area is (root number 3) 4 sides of the square of the length, and the pyramid volume is 1 3 The base area times the height.