Eight years of math problems to find answers to 1 and 2 .

BC ef , angular BCA=angular CAF=60;

ab fd, angular fca = angular bac = 60

In the triangle FCA, the angle CFA=180-60-60=60 is the same as ABE and BCD are equilateral triangles.

So def is an equilateral triangle.

a is a real root of the equation x squared - 2006x+1=0 a 2-2006a+1=0

a+(1 a)-2006=0 (left and right sides divide a) a+(1 a)=2006

a^2-2005a+2006/(a^2+1)=a^2-2005a+(2006/a)/([a+(1/a)]=a^2-2005a+(1/a)

2006a-1-2005a+(1/a)

a+(1/a)-1

Because x2-2006x+1=0, so x2-2006x=-1,a2+1=2006a, so a2-2005a+a2+1 2006=a-1+1 a and a2-2006a+1=0 both sides are divided by a, then a+1 a =2006, so a2-2005a+a2+1 2006=a-1+1 a=2005

1. The discriminant formula of the root = m -4 (2m-n) = m -8m + 4n = 01 is a root of this equation, and there is 1+m+2m-n=1+3m-n=0 The solution of the two formulas is m=-2, n=-5

2. Original price = 100 (1-10%) = 1000 9 about = 111 yuan.

3. The ** yield of Mr. Zhang in 2001 is x

10+10x-5)*(1+x)=

5+15x+10x²=

10x² +

Solution: x= or x= negative value, rounded).

So Mr. Zhang's ** yield in 2001 was.

Question 1: The answer is written on the other two sides as or .

Question 2: The bottom angle is 65 degrees, and the top angle is 50 degrees.

The second is the question of divination.

Solution: Known, 3a+2b+c=4....①，2a+b+3c=5…,2- get,a+5c=6,a=6-5c, 2- 3,b-7c=-7,b=7c-7,and already know that a, b, and c are non-negative real numbers,so,6-5c 0,7c-7 0,can obtain,1 c 6 5 ,s=5a+4b+7c,5 (6-5c)+4 (7c-7)+7c,10c+2,so 10 10c 12,12 10c+2=s 14, i.e., m=14,n=12,n-m=-2

Question 1. 3x-1)/2-7/3≥x-(5+2x)/33x/2-17/6>=x/3-10/6

9x-17>=2x-10

7x>=7

x>=1

x-3|-|x+2|

x=1 The maximum value is p=-1

x>=3 The minimum value is q=-5

The spike value of PQ = 5