Observe the following equation: 1 2 3 4 1 25 5

1) The product of 4 consecutive positive integers plus 1 = (the product of the first and last two numbers in 4 consecutive positive integers plus 1) 2) n(n+1)(n+2)(n+3)+1=[n(n+3)+1] =(n +3n+1).

3) n(n+1)(n+2)(n+3)+1[n(n+3)][n+1)(n+2)]+1(n²+3n)(n²+3n+2)+1

n²+3n)²+2(n²+3n)+1

n²+3n+1)²

1) The multiplication of 4 adjacent natural numbers plus 1 is the square of a number (2) n(n+1)(n+2)(n+3)+1=(n +3n+1).

3) Proof of: n(n+1)(n+2)(n+3)+1[n(n+3)][n+1)()n+2]+1(n+3n)(n+3n+2)+1

n²+3n)²+2(n²+3n)+1

n²+3n+1)²

1) The sum of the product of four consecutive integers and 1 is the square of an integer.

2) n(n+1)(n+2)(n+3)+1=(n +3n+1) 3) Prov: n(n+1)(n+2)(n+3)+1【n(n+3)][n+1)()n+2]+1(n +3n)(n +3n+2)+1

n²+3n)²+2(n²+3n)+1

n²+3n+1)²

Multiplying 4 adjacent natural numbers by 1 is the square of a number.

nx(n+1)x(n+2)x(n+3)+1=cxcn*(n+3)=n 2+3n=(n 2+3n+1)-1n+1)*(n+2)=n 2+3n+2=(n 2+3n+1)+1 so that c=n 2+3n+1, then the conclusion in (2) is true.

So it was proven.

a * b = c^2 - d^2

a+9)*(b+11)=(c+10)^2-(d+1)^2a+9+8)*(b+11+12)=(c+10+10)^2-(d+1+1)^2

The next formula is the age of Lu Chunyu.

(1) Please write the fourth equation according to the above rule: 4 6-5 =-1(2) Represent this law with a letter formula: (a-1)(a+1)-a =-1;

3) The formula written in the first question must be true.

Because: (a-1)(a+1)=a-1

So: (a-1)(a+1)-a = a -1-a =-1

1/√3x+y-2=0

y=-1/√3x+2

The slope is -1 3

2x is -2 3=-2 3 3

So it's y+3=-2 3 3(x-2).

That is, 2 3x+3y-4 3+9=0

Buy fresh, add concentration, buy one.

Your question is equivalent to assuming a+b+c=90°, then there is tana*tanb+tana*tanc+tanb*tanc=1

This can be demonstrated as follows:

Because tana=cot(90°-a), a+b+c=90°, tan(a+b)=(tana+tanb) (1-tana*tanb), so.

tanc=tan(90°-a-b)=cot(a+b)=1/tan(a+b)=(1-tana*tanb)/(tana+tanb)

So, tana*tanb+tana*tanc+tanb*tanc=tana*tanb+(tana+tanb)tanc

tana*tanb+(tana+tanb)*[1-tana*tanb)/(tana+tanb)]

tana*tanb+[1-tana*tanb]

The one upstairs just didn't write it clearly in some places.

The law is: n + n (n 3-1)) = n n (n 3-1) proves that the left side of the equation is dismantled by the root macro friend number = (n 4-n + n) (n 3-1) = n 4 (n 3-1).

Extracting an n 3 will allow you to know that the equation is true.

Well. That's it, I hope so

Analysis: According to the given equation, find out the law, and get the nth equation is (n+2)2-n2=4(n+1), and then substitute n=5

Answer: Solution; ①32-12=4×2

The nth equation is (n+2)2-n2=4(n+1), then the fifth equation is: 72-52=4 6

So the answer is; 72-52=4×6．

Comments: This question examines the change of numbers, and the key is to find out the law of change of numbers through the observation of the great mind, and the nth equation is (n+2)2-n2=4(n+1).