It is known that two α, β of the quadratic equation an X & # 178; - an + 1 x + 1 = 0 (n ∈ n *) satisfy 6 α - 2 α β + 6 β = 3 and A1 = 1 (1) Let an denote an + 1; (2) Verification: the sequence {An-2 / 3} is an equal ratio sequence;

It is known that two α, β of the quadratic equation an X & # 178; - an + 1 x + 1 = 0 (n ∈ n *) satisfy 6 α - 2 α β + 6 β = 3 and A1 = 1 (1) Let an denote an + 1; (2) Verification: the sequence {An-2 / 3} is an equal ratio sequence;

a+b=(an+1)/an
ab=1/an
6α-2αβ+6β=3
6(an+1)/an-2/an=3
an+1=an/2+1/3
(an+1)-2/3=(an-2/3)/2
((an+1)-2/3):(an-2/3)=1/2
So the sequence {An-2 / 3} is an equal ratio sequence

On the solution of quadratic equation
It is known that the perimeter of Δ ABC is 5K, the product of two sides of a, B, C is 4 & # 178;, and the equation x & # 178; - 2kx + A & # 178; = 0 about X has two equal real roots

Discriminant = 4k2-4a2 = 0 K = a (impossible to be equal to - a) B + A + C = 5A B + C = 4A C = 4a-b
AB = 16 or a (4a-b) = 16 or B (4a-b) = 16

The hypotenuse of a right traingle is 17cm long.Another side of the triangle is 7 cm longer than the third side.Determine the unknown side lengths.

8cm,15cm,17cm
x^2+(x+7)^2=17^2
The solution is x = 8

Solving mathematical quadratic equation
It is known that the radius of circle C is 5, and circle C passes a (0, - 2) B (5,3). Find the equation of circle C. let the equation be (x-a) square + (y-b) square = 25, and then substitute two points into x, Y. how to solve the equation and find the process

(0-A) square + (- 2-B) square = 25
(5-a) square + (3-B) square = 25
Subtraction of two formulas
a+b=3
b=3-a ③
Bring (3) into (1)
Bsquare-b-6 = 0
So, B = 3 or B = - 2
Substituting ③
A = 0 or a = 5

How many kilometers per hour is 100 yards?

100 yards = 100 miles = 100 km / h = 100 km / h

36 × 57 / 79 + 57 × 43 / 79 (simple calculation)
Hurry

36×57/79＋57×43/79
=36×57/79＋43×57/79
=（36+43）×57/79
=79×57/79
=57

Given 2x + 2y-4z = 0, 2x + 4Y + 5Z = 0, find the value of X + y + Z / X-Y + Z

This problem does not have to work out x, y, can also be solved
（1）2x+2y-4z=0
（2）2x+4y+5z=0
(2) - (1): 2Y + 9z = 0, that is, 2Y = - 9z
(1) It can be concluded that x + y = 2Z
So x + y + Z = 3Z
Then X-Y + Z = (x + y + Z) - 2Y = 3Z + 9z = 12z
It is easy to get x + y + Z / X-Y + Z = 3Z / 12z = 1 / 4

If the area of a rectangle is a ^ 3-2a ^ 2 + A and the width is A-1, what is the length of the rectangle?
I think the answer is a (a - 1), but I don't know how

The length of a rectangle is equal to:
（a³-2a²+a)÷(a-1)
=[a(a²-2a+1)]÷(a-1)
=[a(a-1)²]÷(a-1)
=a(a-1)

Factorization 2x ^ 2-3 =?

2x^2-3=(√2x+√3)(2x-√3)

Given that the point P (x, y) moves on the circle (X-2) square + (Y-2) square = 2, the minimum value of X / y is
There is also this problem, to build a cuboid uncovered pool with a volume of 200 cubic meters and a depth of 2 meters, the cost of the pool wall is 80 yuan / square meter, and the cost of the pool bottom is 120 yuan / square meter: suppose the bottom length of the pool is x, and the cost is f (x). Try to find the minimum value of F (x)?
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CTG (75 degrees)