Try to explain: the sum of the product of four continuous integers and 1 must be a complete square number

Try to explain: the sum of the product of four continuous integers and 1 must be a complete square number

Suppose the four numbers are:
(x-1),x,(x+1),(x+2)
Then:
(x-1)x(x+1)(x+2)+1
=(x^2-1)(x^2+2x)+1
=x^4+2*x^3-x^2-2x+1
(x^2+x-1)^2.
So the product of four consecutive integers plus one must be a complete square

A passenger car and a freight car leave the two cities at the same time. It is known that the passenger car travels 55 kilometers per hour. The ratio of the speed of the passenger car to that of the freight car is 11:9. When the two cars meet five hours later, how long is the railway between the two cities?

（55+55×9/11）×5
=100×5
=500 km

M / 2-N / 2 = 2m + 3N = 4 solution equation

m/2－n/2＝2
2m-2n=4
2m=2n+4
2n+4+3n=4
n=0
2m=0+4=4
m=2

What's the speed of cheetah per hour?

120KM

The cubic sum of any natural number can be written as the sum of a series of continuous odd numbers. For example, the cubic power of 4 = 13 + 15 + 17 + 19 = 64. What is the odd sum of the cubic power of program n?

=n(1+3+5+...2n-1)

Words line up. Sun, universe, galaxy, moon, earth

From big to small: universe, galaxy, sun, earth, moon,

Solving equation half x minus 25% = 10

1/2x-25%=10
0.5x-0.25=10
0.5x=10+0.25
0.5x=10.25
x=10.25÷0.5
x=20.5

If there is friction, there must be elasticity?
When an object slides down from the wall vertically, the friction force rises. What is the direction of the elastic force?

The elasticity is perpendicular to the wall
If an object slides freely from a vertical wall without pressure, there is no friction,
It is only affected by gravity
If there is friction, there must be elasticity. Elasticity is one of the conditions for friction

If the fractional equation x minus 1 / 6 is equal to X (x minus 1) x plus 3 minus x k, what is the range of K?

6 / (x-1) = (x + 3-K / x) / [x (x-1)] [x ≠ 0 and X ≠ 1] 6 / (x-1) = {x [3 / x + 1-k / (x quadratic)]} / X (x-1) 6 / (x-1) = [3 / x + 1-k / (x quadratic)] / (x-1) 6 = [3 / x + 1-k / (x quadratic)] 6x2 power = 3x + X quadratic - K 5x quadratic - 3x + k = 0 [x ≠ 0 and X ≠ 1] when x = 0, k = 0, when x = 1, k = 2, K value range is any real number of K ≠ 0, K ≠ 2

The passenger and freight cars start from the two places 400 kilometers away at the same time and travel in opposite directions. The passenger cars travel 80 kilometers per hour, and the freight cars travel 80 kilometers per hour
70 km. A few hours later, the two cars are 100 km apart

After X hours, the distance between the two vehicles is 100 km
80x+70x+100=400
x=2