Using a simple method to calculate the square of 2005 Forget about the complete square formula or the square difference formula

Using a simple method to calculate the square of 2005 Forget about the complete square formula or the square difference formula

solution
2005²
=(2000+5)²
=2000²+2×5×2000+5²
=4000000+20000+25
=4020000+25
=4020025

Square-16 of 1996 (calculated by simple algorithm)

1996^2-16=1996*1996-4*4
=(1996+4)*(1996-4)
=2000*1992
=3984000
This is called "square difference formula", which should be the content of junior high school
a*a-b*b=(a+b)*(a-b)

What is the meaning of this ancient poem?

In the Song Dynasty, there is only a river between Jingkou and Guazhou, and Zhongshan is only separated by several mountains. The spring breeze is green on the South Bank of the river. When will the moon shine on me? Note: the poet passed by Guazhou by boat, missing the former residence of Jinling (Nanjing), and wrote this poem

It is known that the line y = KX + 3 and the ellipse x2 / 9 + Y2 / 4 = 1 have a common point. Try to determine the value range of K

∵ straight line y = KX + 3 and ellipse x2 / 9 + Y2 / 4 = 1 have common points ∵ equations: y = KX + 3 ···················································· (1) x2 / 9 + Y2 / 4 = 1 ··································

The surface area of a cuboid is 944dm & # 178;, the bottom area is 192 square centimeters, the perimeter of the bottom surface is 56 decimeters, and the cuboid volume is cubic decimeters
The surface area of a cuboid is 944dm & # 178;, the bottom area is 192 square decimeters, the perimeter of the bottom surface is 56 decimeters, and the cuboid volume is cubic decimeters

Height (944-192 * 2) / 56 = 10 decimeters
Volume 192 * 10 = 1920 cubic decimeter

Simplification: specific steps of sin ^ 2 α cos ^ 2 β - cos ^ 2 α sin ^ 2 β + cos ^ 2 α - cos ^ 2 β,

sin^2αcos^2β-cos^2αsin^2β+cos^2α-cos^2β
=sin^2αcos^2β-cos^2β-cos^2αsin^2β+cos^2α
=(sin^2α-1)cos^2β-cos^2α(sin^2β-1)
=-(1-sin^2α)cos^2β+cos^2α(1-sin^2β)
=-cos^2αcos^2β+cos^2αcos^2β
=0

Given that there is only one circle passing through points a (0, 1), B (4, a) and tangent to X axis, the value of a and the equation of the corresponding circle are obtained

Consider two cases: (I) let the center coordinate of the circle be (x, y), when point B is the tangent point, B is on the x-axis, so a = 0. Then B (4, 0), so the midpoint coordinate of AB is (2, 12), and the slope of the straight line AB is 1 − 00 − 4 = - 14, then the slope of the vertical line AB is 4, so the equation of the vertical line AB is Y-12 = 4 (X-2) and x = 4, so the equation of the circle is: (x-4) 2 + (Y − 172) 2 = (172) 2; (II) when a = 1, AB is parallel to X axis, then the vertical equation of AB is x = 2, let the center coordinate of the circle be (2, y), according to Pythagorean theorem: y2 = 22 + (Y-1) 2, the solution is y = 52, so the equation of the circle is: (X-2) 2 + (Y − 52) 2 = (52) 2 The range is: (X-2) 2 + (Y − 52) 2 = (52) 2

The function y = 2x & # 178; + BX + C passes through (1,2) (0,4) point 1, finds the analytic expression of quadratic function 2, when the independent variable x takes value in what range, y follows X
3. Does the quadratic function have a maximum or a minimum? If so, when x takes what value, does the function get the maximum or the minimum? And find out the maximum and the minimum

If you substitute x = 1, y = 2 into the function y = 2x & # 178; + BX + C, and then substitute x = 0, y = 4 into this function, you can easily get the value of B and C. Therefore, this parabola analytical formula with opening upward has been obtained
You can use it as a formula, or an ordinate formula with the axis of symmetry and the vertex of a parabola
x=-b/(2a),y=(4ac-bb)/(4a).
The value of Y is the minimum
When x is larger than the abscissa of the axis of symmetry, the function increases with the increase of X (increasing function)
On the left side of the axis of symmetry, it is a decreasing function
It makes sense to do it yourself. Right?

8 times of a number is 1.2 less than 27.2. What is the number? (list the equation and find the solution of the equation)

27.2-8x=1.2
8x=26
x=3.25

If f (x) satisfies f (2x-1) = x + 1, then f (3) is equal to?
I didn't even understand the title. Who told me the relationship between the functions in the title

Let me tell you something about it
Since it's a function, no matter how many values x takes, the function holds, and both sides are equal
First of all, the X in the left () represents the independent variable, and the X + 1 on the right = is the value of the independent variable after the function relationship
In the question: what is f (3) equal to? It is equivalent to the requirement that 2x-1 is 3 at the moment. What is your corresponding function value?
Because there is such a relationship, f (2x-1) = x + 1, so x = 2, satisfied. What I want is what they wrote. I won't write any more. I'll just tell you what happened