For quadratic equation x & sup2; + (A & sup2; + 1) x + A-2 = 0, if one root is larger than 1 and the other root is smaller than - 1, then the value range of a is Such as the title

For quadratic equation x & sup2; + (A & sup2; + 1) x + A-2 = 0, if one root is larger than 1 and the other root is smaller than - 1, then the value range of a is Such as the title

Let f (x) = x ^ 2 + [(a ^ 2) + 1] x + A-2, f (x) be a parabola with opening upward. According to the meaning of the topic, the intersection of parabola and X axis is > 1 and < - 1 respectively, and the parabola symmetry axis X = - (a ^ 2 + 1) / 2 is in the interval [- 1,1], that is, f (- 1) < 0 - 1 ≤ - (a ^ 2 + 1) / 2 ≤ 1, f (1) < 0 1 + (a ^ 2 + 1)

It is proved that if M and N are rational numbers, then the roots of the quadratic equation 2mx & # 178; - (3m-2n) x-3n = 0 are rational numbers
In addition, if ad BC = 1, then a & # 178; + B & # 178; + C & # 178; + D & # 178; + AB + CD ≠ 1

Question 1: using the universal formula X1 = 3 / 2, X2 = - N / M
Both are rational numbers
The second question: A & # 178; + B & # 178; + C & # 178; + D & # 178; + AB + CD = (2a & # 178; + 2B & # 178; + 2C & # 178; + 2D & # 178; + 2Ab + 2cd-2) / 2 + 1
Let 2 = 2 (AD BC) = [(a + b) & #178; + (c + D) & #178; + (A-D) & #178; + (B + C) & #178;] / 2 + 1
≥1
Only if a + B = 0, C + D = 0, A-D = 0, B + C = 0 = 1
That is, a = b = C = D = 0
Since ad-bc = 1, a = b = C = D = 0 does not hold
So a & # 178; + B & # 178; + C & # 178; + D & # 178; + AB + CD > 1
That is, a & # 178; + B & # 178; + C & # 178; + D & # 178; + AB + CD ≠ 1

Let a set of data x1, X2, X3, x4 The average number of, xn is 5, and another set of data y1y2y3y4 The average of YN is - 2
So 5x1 + 2y1, 5x2 + 2Y2 The average of 5xn + 2yn is

5*5+2*(-2)=21

The equation for finding the chord with (1,1) as the midpoint when the straight line y = X-2 and the parabola y ^ 2 = 2x intersect at a and B points

Let a (x1, Y1), B (X2, Y2), the slope be K
(1,1) is the midpoint of ab
∴y1+y2=2
y1^2=2x1, y2^2=2x2
Subtraction:
y1^2- y2^2=2(x1-x2)
(y1-y2)(y1+y2)=2(x1-x2)
(y1-y2) / (x1-x2) = 2 / (Y1 + Y2) = 1, that is, k = 1
The equation is X-Y = 0

Calculation formula for the velocity V of the cylinder
Single rod piston cylinder, the reference book formula is v = q / a times the volumetric efficiency of the cylinder, please help us to decompose the formula and value of volumetric efficiency! The inner diameter of the cylinder is 50, the stroke is 50, the air supply pressure is 7 kg / cm2!
It's not the cylinder of the car, it's the cylinder of stamping workpiece in the industry, which can be controlled by a solenoid valve! I understand that the volumetric efficiency here is the ratio of the compressed air volume of the cylinder to the volume of the cylinder! Is the unit a percentage? How to calculate and get the value?

Find the rule 2187729243,81, (), (), 3,1

27,9 (3 times less each)

dy/dx=-y y(0)=1,

Separate variables. Dy / y = - DX, integral LNY = - x + C, x = 0, y = 1, substitute, C = 0, so LNY = - x, y = e ^ - X

How many tons is a cubic meter of sand

It is generally required that the bulk density of sand for construction is 1350-1450kg / m3, from which the weight of one cubic meter of sand can be calculated to be about 1.35-1.45t

Some problems of complete square formula
①（-m-n）（-m+n）
②（-m-n）（m+n）
③ Square of a + 6A + () = square of (a +)
④ 4X squared - 20x + () = (2x -) squared
⑤ Square of a + square of B = (a-b) square + ()
⑥ Square of (X-Y) + () = square of (x + y)

1.(-m)^2-n^2
2.-(m+n)^2
3.a^2+6a+9=(a+3)^2
4.4x^2-20x+25=(2x-5)^2
5.a^2+b^2=(a-b)^2+2ab
6.(x-y)^2+4xy=(x+y)^2

(x + y-xy) / (x + y + 2XY) = (y + z-2yz) / (y + Z + 3yZ) = (Z + x-3zx) / (Z + X + 4zx), and 2 / x = 3 / Y-1 / Z, then XYZ =?
See, it's 2 / x = 3 / Y-1 / Z

(x + y-xy) / (x + y + 2XY) (divide by XY) = (1 / x + 1 / Y-1) / (1 / x + 1 / y + 2) = (2 / x + 2 / Y-2) / (2 / x + 2 / y + 4) = (5 / Y-1 / Z-2) / (5 / Y-1 / Z + 4) = 1-6 / (5 / Y-1 / Z + 4); similarly, (y + z-2yz) / (y + Z + 3yZ) = (1 / y + 1 / Z-2) / (1 / y + 1 / Z + 3) = 1-5 / (1 / y + 1 / Z + 3); (Z + x-3zx) / (Z +