Six riddles for 50 people to guess, each riddle guess once, a total of 178 times, known that each person guessed at least two, only two of 16 people, only four of 9 people, only three and only five of the same number. So how many people can guess all six riddles correctly? 2 6 8 n m 20

Six riddles for 50 people to guess, each riddle guess once, a total of 178 times, known that each person guessed at least two, only two of 16 people, only four of 9 people, only three and only five of the same number. So how many people can guess all six riddles correctly? 2 6 8 n m 20

Let x person guess 6 riddles correctly. According to the meaning of the question, the number of times to guess 6 riddles correctly is: 6x, the number of times to guess 5 and 3 riddles correctly is: (50-16-9-x) × 4, the number of times to guess 4 riddles correctly is: 9 × 4 = 36, the number of times to guess 2 riddles correctly is: 16 × 2 = 32, 6x + (50-16-9-x) × 4 + 36 + 32 = 178, & nbsp; & nbsp; & nbsp; & nbsp; 6x+（25-x）×4+36+32=178，          6x+100-4x+36+32=178，                   2x+168=178，                It is 168-168-168-168-178-168-168, which is 168-168-168-168-168-168, and the & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & & & nbsp & nbsp & nbsp & & 5. Answer: five of the six riddles are correct

Solve the following equation (process) in an appropriate way
(1) 3x & # 178; = 4x (factorization) (2) 4 (x-1) &# 178; = 49 (direct open method)
(3) 3x & # 178; - 5x + 1 = 0 (formula method)

(1) 3x & # 178; = 4x (factorization)
3x²-4x=0
x(3x-4)=0
x=0 or x=4/3
(2) 4 (x-1) & 178; = 49 (direct open method)
（x-1）²=49/4
x-1=±7/2
x=9/2, or x=-5/2
(3) 3x & # 178; - 5x + 1 = 0 (formula method)
x=[-b±√(b^2-4ac)]/2a
x=[5±√(25-12)]/6
x=(5±√13)/6

Solve the following equation in an appropriate way
（1）a²-4a-21=0
（2）(x+3)²=-x（x+5)
(3) 1 / 2 (2x-5) & # 178; - 8 = 0

1、（a-7)(a+3)=0
a=7
a=-3
2、x²+6x+9=-x²-5x
2x²+11x+9=0
(2x+9)(x+1)=0
x=-9/2
x=-1
3、（2x-5)²=16
2x-5=±4
2x-5=4,x=9/2
2x-5=-4,x=1/2

A high school mathematics problem (on the circle and linear equation), online and so on!
The two diagonals of rectangular ABCD intersect at M (2,0), the linear equation of AB is x-3y-6 = 0, the point t (- 1,1) is on the line where ad side is located (1) find the linear equation where ad side is located (2) find the equation of circumscribed circle of rectangular ABCD
[simple process]

1
kAB=1/3,KAD=-3
y-1=-3(x+1)
3x+y+2=0
two
LianLi 3x+y+2=0,x-3y-6=0,
x=0,y=-2
r^2=(2-0)^2+(0+2)^2=8
(x-2)^2+y^2=8