1. Given that the opposite number of X is 3, the absolute value of Y is 4, and the sum of Z and 3 is 0, try to find the value of XY + YZ + XZ 2 calculation: (1 / 2005) (1 / 2004) (1 / 2003)... (2 / 1)

1. Given that the opposite number of X is 3, the absolute value of Y is 4, and the sum of Z and 3 is 0, try to find the value of XY + YZ + XZ 2 calculation: (1 / 2005) (1 / 2004) (1 / 2003)... (2 / 1)

Topic 1: XY + YZ + XZ = y (x + Z) + XZ
X = - 3, y = 4 or - 4, z = - 3
When the answer is 1 y = 4, the answer is 27
When 2Y = - 4, the answer is 45
The second topic is to spread the topic
If xy = a, XZ = B, YZ = C, and they are not equal to zero, then how much is x + y + Z?
∵xy=a,xz=b,yz=c,∴y=a/x z=b/x ∴yz＝ab／x²＝c ∴x²=ab／c
∵xy=a,xz=b,yz=c,∴x=a/y z=c/y ∴xz＝ac／y²＝b ∴x²=ac／b
∵xy=a,xz=b,yz=c,∴x=b/z y=c/z ∴xy＝bc／z²＝b ∴z²=bc／a
∴a²＋b²＋c²＝ab/c+ac/b+bc/a
xy*xz/yz+xz*yz/xy+xy*yz/xz
=x²+y²+z²
=ab/c+bc/a+ac/b
=(a²b²+b²c²+a²c²)/abc
Just compare them for a + B + C
xy*xz/yz+xz*yz/xy+xy*yz/xz
=x²+y²+z²
=ab/c+bc/a+ac/b
=(a²b²+b²c²+a²c²)/abc
∵ xy = a, XZ = B, YZ = C, ∵ y = A / x, z = B / X ∵ YZ = AB / X & # 178; = C ∵ X & #... Expansion
xy*xz/yz+xz*yz/xy+xy*yz/xz
=x²+y²+z²
=ab/c+bc/a+ac/b
=(a²b²+b²c²+a²c²)/abc
∵xy=a,xz=b,yz=c, ∴y=a/x z=b/x ∴yz＝ab／x²＝c ∴x²=ab／c
∵xy=a,xz=b,yz=c, ∴x=a/y z=c/y ∴xz＝ac／y²＝b ∴x²=ac／b
∵xy=a,xz=b,yz=c, ∴x=b/z y=c/z ∴xy＝bc／z²＝b ∴z²=bc／a
｛ A & ｛ 178; + B & ｛ 178; + C & ｛ 178; = AB / C + AC / B + BC / A
For any real number x, inequality-3 is known
If x ^ 2-x + 1 is always greater than 0, then:
x^2+ax-20,
If f [(a + 2) / 2] = 4 - (a + 2) ^ 2 / 4 > 0, that is - 60,
If G [(3-A) / 8] = 1 - (3-A) ^ 2 / 16 > 0, that is - 1
If the image of the quadratic function passes through the origin and the point (- 4,0), then the equation of the symmetry axis of the image of the quadratic function is
The two points (0,0) and (- 4,0) that this topic passes through are exactly the two intersections of the parabola and the x-axis
The axis of symmetry is the midpoint of the intersection
Then the axis of symmetry x = (1-4) / 2 = - 2
If a parabola passes through points (0,0) and (- 4,0), then the axis of symmetry of the parabola is x = - 2
The parabola intersects the X axis at (0,0) and (- 4,0). The two intersections of the parabola and the x-axis are symmetric about the axis of symmetry, that is, the intersection of the axis of symmetry and the x-axis should be the midpoint-2 of 0 and-4. Therefore, the symmetry axis equation of the image of the quadratic function is x = - 2
The equation of symmetry axis of quadratic function is as follows
X = (x1 (a solution to the left) - x2) / 2
So the axis of symmetry is x = - 2
Try to determine the value range of real number m so that [(a + 1) x2 + ax + a] / [x2 + X + 1] > m is an absolute inequality
[(a+1)x2+ax+a]/[x2+x+1]>m
a+x^2/(x^2+x+1)>m
x^2/(x^2+x+1)>m-a
Because x ^ 2 > = 0, x ^ 2 + X + 1 = (x + 1 / 2) ^ 2 + 3 / 4 > 0
So x ^ 2 / (x ^ 2 + X + 1) > 0
To make the above inequality absolute, we only need m-a
If the image of a quadratic function passes through the origin and the point (- 4,0), what is the equation of the symmetry axis of the image of the quadratic function
x=-2
The image of quadratic function is a parabola, and it passes through the origin (0,0) and (- 4,0) and is symmetric about x = - 2, so the equation of axis of symmetry is x = - 2.
It's x = - 2. Let's review the basic knowledge of quadratic function.
The two parts of the equation x square - MX + 1 = 0 are a and B, and a > 0,1
1. If the product of two is 1, if one is greater than 1, then the other must be less than 1
So the two roots are not equal, △ > 0
m> 2 or M
Y = x ^ 2-mx + 1 opening up
Judging m ^ 2-4 > 0
x1+x2=m>0
m>2...1）
a=0,y>0
b=1,y0
1-m+10.....3）
4-2m+1>0,m
The symmetry axis equation of the image of quadratic function y = x square + 2x + 2
y=x²+2x+1+1
=(x+1)²+1
=[x-(-1)]²+1
So the axis of symmetry is x = - 1
Axis of symmetry equation: x = - 1
The equation 2x (mx-4) = x Square-6 of X has two real roots, and the maximum integer value of M is obtained
The original equation is reduced to (2m-1) x & sup2; - 8x + 6 = 0, so 2m-1 ≠ 0, discriminant ≥ 0, the solution is 48m-88 ≤ 0, m ≤ 88 / 48, and m ≠ 1 / 2. So the maximum value of M is 1
From 2x (mx-4) = x ^ 2-6, (2m-1) x ^ 2-8x + 6 = 0,
And the equation about X has two real roots
∴2m-1≠0,△=(-8)^2-4*6*(2m-1)≥0
Then, m ≠ 1 / 2, m ≤ 11 / 6
The maximum integer value of M is 1
The equation of symmetry axis of image of quadratic function y = 2 ((x-4)) square + 4 is
Expand the quadratic expression to get a = 2, B = - 16
X=-b/2a=-(-16)/2*2=4
So the equation of axis of symmetry is: x = 4