8. Quadratic equation math problems? Ask for more details! Thank you!

Because (x-a)(x-b)=1, (x-a) and (x-b) are reciprocal to each other, substituting x1 and x2 into the equation, there are (x1-a) (x1-b) = 1, (2x-a) (x2-b) = 1, that is, (x1-a) = 1 (x1-b), (x2-a) = 1 (x2-b), both sides of the equation are positive or negative, indicating that x1 and x2 cannot be between a and b. If both are smaller than a or both are larger than b, the original equation will not have two different roots, so it can only be x1

Solution ratio: 2: 1/3 x 4/5 = 15/5 72/16 = x: 1/6 = 7: 1/5 20 8 = x 24/2

X out of 4

x: 3/4 = 1/2: 1/4

2/8 = 3/x

4/9: 1/6 = x:6

1/4: 1/6 = x: 1/20

x 10 = 3 out of 5

8 and 3/4: x = 7:1

x: 2/11 = 11:5

1:2 and 1/2 = 5/2:x

240:x=4:3

x: 13/15 = 4/13

3/4: x = 3/5

I'll explain when you're done writing.

Student, let me help you prove it, you can disassemble the formula to the left of the equality sign of the original equation, and move the 1 to the right of the equality sign to the left of the equality sign, and you can become x squared—(a+b)x--1=0

Because x1 and x2 are the two roots of the original equation, they must satisfy x1+ x2=a+b (this is a theorem, and your teacher will talk to you when he talks about a quadratic equation, which is very useful). And option A is obviously X1+ X2 "A+B

I don't know how far your teacher has already spoken, so please forgive me if I don't solve your problem.

If you still don't understand, feel free to ask!

The result of the difference between the two parentheses must be either negative or positive in order to satisfy the equation, in aIn the case of

1) Here the first and last two terms are the squares of the two numbers x and m, so the middle term is 2 times the product of x and m added or subtracted

Solution: x2+2mx+4-m2 is a completely flat method, x2+2mx+4-m2=(x m)2,4-m2=m2,m= 2, i.e. m1=2, m2=-2

2) Use the cross multiplication ruler to leak.

Solution: The original equation becomes [mx-(2m-3)][mx-(m-5)]=0, m≠0x1=2-3m, x2=1-5m

If x1 is an integer, then 3m is a vibrillator macro number, m=l or m=3 If x2 is an integer, then 5m is an integer

m = 1 or m = 5

Answer: The value of m is 1 or 3 or 5

1) That is, the discriminant formula is 0, delta=4(m 2-4+m 2)=8(m 2-2)=0, and m = 2 or - 2

2) When m=0, the equation is; 15=0, obviously the mausoleum sedan chair is not a ruler.

m<>0, m 2x 2-(3m 2-8m)x+2m 2-13m+15=0, right? It can be broken down as follows:

m^2x^2- (3m^2-8m)x+(2m-3)(m-5)=0mx-(m-5)][mx-(2m-3)]=0x1=(m-5)/m=1-5/m

x2=(2m-3)/m=2-3/m

Therefore, in order for x1 and x2 to have an integer, it is necessary to talk about the factor of 3 or 5 m, that is, m can be: 1, -1, 3, -3, 5, -5

[(x+1)(x+4)]*x+2)(x+3)]=(x^2+5x+6)*(x^2+5x+4)=120

Let x 2+5x=y, then (y+6)(y+4)=

y 2 + 10 y - 96 = 0, (y - 6) (y + 16) = 0, the solution is y = 6 or y = -16

y=6 is substituted into the equation and x=-6 or x=1 is solved

y=-16 is substituted into the equation, x 2 + 5x + 16 = 0, (x + equation does not hold, so there is no solution.)

（x+1)(x+2)(x+3)(x+4)=[(x+4)（x+1)][x+2)(x+3)]

x 2+5x+4)(x 2+5x+6) = 120 reams x 2+5x=a then.

a+4)(a+6)=120 i.e.

a 2+10a-96=0 i.e.

a+16)(a-6)=0.

a1=-16 a2=6 i.e.

x 2 + 5 x + 16 = 0 or x 2 + 5x + 6 = 0 solution (x 2 + 5x + 16 = 0 I won't solve it, you can solve it yourself.) )x1= x2=

x3=-2 x4=-3

∵2×3×4×5=120

x=1or-6

The words of thought ... Let's start with the 120 decomposition factor. You can solve it. It is difficult to consider the positive and negative commutation method.

The May Rise is 500 (1-10%) = 450, and the growth rate is x

Then June is 450 (1+x).

July is 450 (1+x) (1+x) = 648

1+x)²=648/450=

1+x=x=20%, so the increase in noise is 20%.

Solution: According to the meaning of the topic, it is obtained:

a-21)（350-10a)=400……（1）a-21=<

From (1): a=25 or a=31

From (2): a=<

So a=25

So it needs to be sold for 25 yuan.

Solution:1The plant was set up.

The percentage of the average two-month increase in production in the six- and seven-year-old bands is x.

500 ( x1 = x2 = rounded).

Answer. 2.Set the price of each Sun Lu piece of goods to be sold at x yuan.

a-21）(350-10a)=400

x1 = 25 x2 = 31 (markup over 20 rounding of the purchase price) 350-10a = 100

1. Solution: The width of the door is x feet, and the height is (x + feet.

According to the title, it gets: ab +bc =ac

i.e.: (x+.)

Solution: x1= x2=

x=not in place.

x=Rounded. So x+ruler).

Answer: The width of the door is a ruler, and the height is a ruler.

2. Solution: Let the width of the cuboid wooden box be x dm then the length is (x+5) dm.

According to the title, it gets: 8x(x+5)=528

x（x+5）=66

x²+5x-66=0

Solution: x1=-11 x2=6

x=-11 does not fit the topic.

x=-11 rounded.

So x+5=6+5=11 (decimeter).

A: The length is 11 dm and the width is 6 dm.

1 ruler = 10 inches, 1 ruler = 1 3 meters = 100 3 cm, 1 inch = 10 3 cm.

Just do the math.

Set the height x and the width y, then there is.

x-y = square of x + square of y = 1

There is only a solution. Question 1: Set the height to x, the width to, and bring y into the following formula!

x squared + (squared = 10 (high squared + wide squared) = 10 to get the specific value of height and width.

The main value is 1 zhang, 1 zhang = 10 feet!

Question 2: Let the length of the cuboid wooden box be x, then the width is x-5Therefore x*(x-5)*8=528, the solution is obtained.

Question 2: Let the length of the cuboid wooden box be x, then the width is x-5Therefore x*(x-5)*8=528The solution yields x=11 or x=-5 (rounding).

It can be set by the title.

x^2-5x+1=(x+a)(x+b)

That is, x 2-5x+1=x 2+(a+b)x+ab is obtained by comparing the coefficients at both ends.

a+b=-5,ab=1

Solving a system of equations is.

The solution method dissolves the kernel as follows, and the first formula is represented by a and b, which is substituted into the second one to solve the one-dimensional dirock digging equation about a.

There is a minimum, a minimum of 1

x²+8x+17

x²+8x+16+1

x+4)²+1

Since (x+4) 0

So (x+4) +1 1, and x +8x+17=1 is the smallest when x=-4.

x²+8x+17

x²+8x+16+1

x+4)²+1

Since (x+4) 0

So (x+4) +1 1, and x +8x+17=1 is the smallest when x=-4.

Set the uphill as x, and the downhill bridge as y

y-3=1/3(x+y)

y+3=x-3

x=21 y=15