Finding the solution of a two dimensional equation in mathematics, junior high school 8th grade math

<> forgot to open the root number in the first question, let's do the math yourself.

The first one of the third question also forgot to open the root number.

Solve the equation using the matching method: the square of x - 3x-1 = 0

Move the constant term to the right of the equation to get the equation: the square of x - 3x=1 Add 9 4 on both sides of the equation at the same time, and get the square of the equation x - 3x+9 4 = 1+9 4 The left side of the equation is perfectly squared, and the equation (x-3 2) square = 13 4 square is obtained, and the equation x-3 2 = positive and negative root number 13 2 solves two unary linear equations x-3 2 = root number 13 2- and x-3 2 = negative root number 13 2--

The solution is x1 = 3 2 + root number 13 2, x2 = 3 2 - root number 13 2 two, the square of x + 4x + 4 = (x + 2) square.

x squared - 5x + 25 4 = (x-5 2) squared.

x squared - quarter x + 1 4 = (x-1 2) squared.

x squared + mx + m squared 4 = (x + m 2) squared.

x squared + b x + b squared (4a squared) = (x + b 2a) squared.

Three, the square of x - 4x-21 = 0

x squared + 3x + 1 = 0

3x squared + 6x-1 = 0

Half x squared - 3x - 5 = 0

x square + 8x = 9984

x=1k+1-3k-3m+4kn=0 (4n-2)k=3m-1

So 4n-2=3m-1=0

So m=1 3, n=1 2

k+1)x-3(k+1 3)x+2k=0, then x1+x2=(3k+1) (k+1).

x1x2=2k/(k+1)

x1=1, so x2=2k (k+1).

1, x 2 + 48x-128 = 0, x 2 + 48x+24 2-128-24 2 = 0, ( 2 means squared, the following is the same), x + 24 ) 2 = 704, x + 24 = 704, x = -24 8 11, x 2-12x+4-9x=0, 9x 2-21x+4 = 0, x = (21 297) 18.

3、（1）(x-1)^2+(-4),2)、(x+p/2)^2+(q-p^2/4).

This is an average growth rate problem, and the basic formula for solving this type of problem is: the final value and the beginning value (1 x)nth power. Here x is the average growth rate and n is the number of consecutive increases.

Solution: Suppose the average monthly growth rate of turnover from March to May is x.

According to the title, yes.

400（1＋10％）（1＋x）^2＝。

Sorted out (1 x) 2.

The solution is x1 and x2 is not in line with the topic, so discard).

A: The average monthly growth rate of turnover from March to May was 20.

8/8 (y+3) y=4/4 (y+3)-2/2 (y-1).

y+3）² 8y=2(y+3)-4(y-1)(y+3)²-2(y+3)+1=8y-4y+4+1(y+3-1)²=4y+5

y²+4y+4=4y+5

y =1y=1, or y=-1

x²-（a+b）x+ab=0

x-a)(x-b)=0

x=a, or x=b

x-a）²=4（x²-a²）

x-a)²=4(x-a)(x+a)

x-a=4(x+a)

3x=-5a

x=-5/3a

The specific answer is troublesome.

In short, it is a shift so that one side of the equation is equal to 0

It's good to use the root finding formula or factoring.

If the length of the chicken farm is x, then the width is (70-x) 2, so the columnable equation is x*(70-x) 2=528, and the solution is x1=48, x2=22, and because the wall is 27 meters long, x=48 should be discarded, so x=22, so the length is 22 meters, and the width is 24 meters.

Solution: Let the side parallel to the wall be x (x is greater than 0 and less than or equal to 27) then the other side is (70-x) 2

According to the title.

x(70-x)/2=528

The solution is x1 = 22 and x2 = 48 (rounded).

then (70-x) 2=24

So the length of the chicken farm is 24 and the width is 22

Solution: If the side length of the vertical wall is a, then the side length of the opposite side of the wall = (70-2a) is 528 square meters.

a*（70-2a）528

a = 11 or 24

a=11, (70-2a)=48>27 rounded a=24, (70-2a)=22

So the length and width are 24, 22

Set length x and width (70-x) 2

Rectangle area: x(70-x) 2=528

x = 22 or 48

But long x<27 (wall length).

Length x = 22 Width (70-22) 2 = 24 and 24 Width.

(x-1) -2=0, so x-1=plus and minus root number 2, i.e. x = plus plus 1 for positive and negative root number 2

Because the passenger car catches up with the truck from behind, the passenger car is faster than the truck speed: let the passenger car speed x meters per second, the truck speed y meters per second, and x is greater than y (the reason is the above line of words) according to the sum of the speed of the two vehicles, you can get x + y = 32According to the intersection time of two cars is 1 minute, it is recommended to make a graph on the map, and it can be concluded that 1 minute is the time to start overtaking and exceed, and the distance is not the sum of the length of the two cars 200 + 280 = 480

Since the passenger car exceeds the truck, the difference between the speed of the two cars is multiplied by 60 seconds (1 minute is equal to 60 seconds) is equal to 480 meters, so the binary equation x+y=32 (x-y)*60=480 can be solved to obtain x=20 (meter seconds) y12 (meter seconds) Answer: The speed of the passenger car is 20 meters and seconds, and the speed of the truck is 12 meters and seconds.

I hope that the landlord will learn and progress, and I hope you will adopt!

Solution: Let the speed of the passenger car be x meters and seconds, then the speed of the truck is (3x 5) meters and seconds, and the equation is listed according to "if the time of the two vehicles is 1 minute": (x-3x 5)*60=200+280

Catch up with the problem) to solve: x = 20 (meter seconds).

So the truck speed is 3x 5 = 12 (m s).

A: The speed of the bus is 20 meters per second, and the speed of the truck is 12 meters per second, I wish you good progress in learning!!

Let S1 = 200m, S2 = 280M, the speed of the passenger car is V1; The speed of the wagon is v2; List the system of equations 1: v1 + v2 = 32 2 formula: v1 60 = v2 60 + s1 + s2, and solve the system of equations to obtain:

v1=20m/s v2=12m/s.Authentic hand counting. Hand hit, let's give points.

Think more.

Specifically, you should be able to do it, so I'll briefly explain it.

Passenger cars are x meters in seconds, and trucks are in Y meters seconds.

x+y=32

x-y)×60=200+280

x=20y=12