After reading the story "on paper", what do you know from it?

After reading the story "on paper", what do you know from it?

So many times, we can't take it for granted. We should learn to be down-to-earth and do things. And sometimes we should learn to be modest and not be blindly arrogant

Application of mathematical factorization
Given that a, B and C are the three sides of △ ABC and satisfy a ^ 4 + B ^ 2C ^ 2 = B ^ 4 + A ^ 2C ^ 2, try to judge the shape of △ ABC

(a^4-b^4)+b²c²-a²c²=0(a²+b²)(a²-b²)-c²(a²-b²)=0(a²-b²)(a²+b²-c²)=0a²-b²=0,a²+b²-c²=0a=b,a²...

Simple application of factorization
(x^2y-xy^2)/(x-y)=______
(a^2-9)/(a+3)=_____
(m^2+2mn+n^2)/(m+n)=_____
(4x^2-4x+1)/(1-2x)
(a^2-64)/(a-8)
(3x^3 y^2+6x^2 y^3)/(x+2y)
(-9m^2+4n^2)/(3m+2n)
(4a^2-20ab+25b^2)/(5b-2a)
(1-16a^4)/(4a^2+1)/(2a+1)
solve equations
x^2+2x=0
9x^2-4=0
-1/2x^2+2x=0
(3a-4)^2=25

x^2y-xy^2)/(x-y)=__ xy(x-y)/(x-y)=xy____
(a^2-9)/(a+3)=__ =(a+3)(a-3)/(a+3)=a-3___
(m^2+2mn+n^2)/(m+n)=__ =(m+n)^2/(m+n)=m+n___
(4x^2-4x+1)/(1-2x)=(1-2x)^2/(1-2x)=1-2x
(a^2-64)/(a-8)=(a+8)(a-8)/(a-8)=a+8
(3x^3 y^2+6x^2 y^3)/(x+2y)=3x^2y^2(x+2y)/(x+2y)=3x^2y^2
(-9m^2+4n^2)/(3m+2n)=(2n+3m)(2n-3m)/(3m+2n)=2n-3m
(4a^2-20ab+25b^2)/(5b-2a)=(5b-2a)^2/(5b-2a)=5b-2a
(1-16a^4)/(4a^2+1)/(2a+1)=(1-4a^2)(1+4a^2)/[(4a^2+1)(2a+1)]=(1+2a)(1-2a)/(1+2a)=1-2a
solve equations
x^2+2x=0
x(x+2)=0
x=0,x=-2
9x^2-4=0
(3x+2)(3x-2)=0
x=-2/3,x=-2/3
-1/2x^2+2x=0
-1/2x(x-4)=0
x=0,x=4
(3a-4)^2=25
(3a-4)^2-25=0
(3a-4+5)(3a-4-5)=0
(3a-1)(3a-9)=0
a=1/3,a=3

Given that n is a positive integer and (4 ^ 7) + (4 ^ n) + (4 ^ 1998) is a complete square number, what is the value of N
The teacher said there were three answers

(4 ^ 7) + (4 ^ n) + (4 ^ 1998) = (2 ^ 7) ^ 2 + (4 ^ n) + (2 ^ 1998) ^ 2 is a complete square
So 4 ^ n = 2 * 2 ^ 7 * 2 ^ 1998 = 4 ^ 1002
So n = 1002

Simple application of factorization
(1-16a to the fourth power) / (4a & sup2; + 1) / (2a + 1)
Solution equation: - 1 / 2x & sup2; + 2x = 0
(3a-4)²=25
Come on, man

(1-16a to the fourth power) / (4a & sup2; + 1) / (2a + 1)
=-(the fourth power of 16a-1) / (4a & sup2; + 1) (2a + 1)
=-(4a²+1)(2a+1)(2a-1)/(4a²+1)(2a+1)
=-(2a-1)
=1-2a
-1/2x²+2x=0
-1/2x(x-4)=0
x=0,x=4
(3a-4)²=25
(3a-4)²-25=0
(3a-4+5)(3a-4-5)=0
3(3a+1)(a-3)=0
a=-1/3,a=3

What is the decomposition of force

If a force acts on an object, its effect on the object is the same as that of other forces acting on the same object at the same time. These forces are the components of that force. For example, fix two rubber ropes on the board and tie two thin wires at the joint of the two ropes

There are several ways to decompose forces?
What is orthogonal decomposition?

When an object is subjected to multiple forces, the resultant force can be obtained by orthogonal decomposition of each force along two mutually perpendicular directions, and then the resultant force can be obtained respectively along these two directions. The orthogonal decomposition method is the basic method to deal with the problems of multiple forces. It is worth noting that when choosing the direction, the force falling on the axis should be as much as possible

What are the principles for the composition and decomposition of forces

They all follow the parallelogram rule

What are the rules for calculating the decomposition of forces

Triangle rule
Please accept

What is the similar triangle method and how to use it?

That is, after a force cross in any direction is decomposed into XY axis, the magnitude and direction of the force and the force become two vertical directions