1 * 2 * 3 * 4 + 1 = 5, 2 * 3 * 4 * 5 + 1 = 11, 3 * 4 * 5 * 6 + 1 = 19, n * (n + 1) (n + 2) (n + 3) + 1 =? (n is an integer) Please explain the idea?

1 * 2 * 3 * 4 + 1 = 5, 2 * 3 * 4 * 5 + 1 = 11, 3 * 4 * 5 * 6 + 1 = 19, n * (n + 1) (n + 2) (n + 3) + 1 =? (n is an integer) Please explain the idea?

The quadratic power of [n * (n + 3) + 1]

Observe the following formats: 1 * 2 * 3 * 4 * + 1 = 5 ^ 2; 2 * 3 * 4 * 5 + 1 = 11 ^ 2; 3 * 4 * 5 * 6 + 1 = 19 ^ 2; judge whether the sum of the product of any four consecutive positive integers and 1 is the square of a positive integer, and explain the reason

Let four consecutive integers be: n-1, N, N + 1, N + 2 (n is an integer)
(n-1)n(n+1)(n+2)+1=(n^2-1)(n^2+2n)
=n^4+2n^3-n^2-2n+1
=(n^2+n)^2-2(n^2+n)+1
=(n^2+n-1)^2

When Xiao Ming read a decimal, he read the decimal point wrong, and the result was 45.8

450.08
four hundred and fifty point zero eight

A and B two cars respectively from AB two places at the same time, meet at 60 kilometers away from a, after meeting, two cars continue to move forward
After arriving at the other party's starting place, return immediately, and find the distance between the two places at 40 km away from B for the second time
It's urgent

60 × 3 = 180 km
Distance: 180-40 = 140 km

Fill in the blanks in Mathematics (rational number)
a. B is a rational number, if = 1, then a 0; if = - 1, then a 0

a,>,a,

The two trains leave 500 kilometers apart at the same time, but they don't meet each other four hours later. They are 20 kilometers apart. It is known that car a travels 65 kilometers per hour, and how many kilometers does car B travel per hour?

(500-20) △ 4 = 480 △ 4 = 120 (km); 120-65 = 55 (km); a: car B runs 55 km per hour

If the average of data 3,6,7,1,3,6 and X is 4, then the median of this group of data is () and the mode is ()

The median is 4.5 and the modes are three and six

Both Party A and Party B travel from city a to city B. Party A rides a bicycle and Party B rides a motorcycle. Party A starts 2 hours and 15 minutes earlier than Party B. Party B walks for 2 hours and is still 11 kilometers behind Party A. Party B walks for another 3 hours, exceeding Party A's 13 kilometers. As a result, Party B arrives in city B 1 hour and 45 minutes earlier than Party A____ Kilometer

Let a's speed be C, B's speed be D, and B's time to B be X
If (2 + 9 / 4) c-2d = 11 3 (d-c) = 11 + 13, then C = 12 and d = 20 can be obtained
According to B arriving in city B 1 hour 45 minutes earlier than a, we can get 20x-12 * (9 / 4 + x) = 7 / 4 * 12 and x = 6
So AB distance = 6 * 20 = 120km

If the arithmetic square root of a natural number is a (a > 1), then the arithmetic square root of two natural numbers adjacent to the natural number is?

The natural number is a-178;
So the adjacent ones are a-178; - 1 and a-178; + 1
So the arithmetic square root is √ (A & # 178; - 1) and √ (A & # 178; + 1)

The distance between the two places is 96 kilometers. A and B run from the two places at the same time and meet each other in 45 hours?

96 △ 45-54, = 120-54, = 66 km; a: car B travels 66 km per hour