It is known that the sum of two natural numbers is 1000 less than their product, and one of the natural numbers is a square number

It is known that the sum of two natural numbers is 1000 less than their product, and one of the natural numbers is a square number

Hello, Zhang Yumeng_ Zhang Yumeng
Let one of the numbers be X & #, and the other be y
Then the countable equation, X & # 178; + y + 1000 = x & # 178; y
That is, X & # 178; Y-X & # 178; - y + 1 = 1001, that is, (X & # 178; - 1) (Y-1) = 1001, that is, (x + 1) (x-1) (Y-1) = 1001
And X + 1, X-1, Y-1 are integers, while 1001 = 7 × 11 × 13
Then x = 12, y = 8, that is, the two numbers are 144 and 8
The larger number is 144

Multiply 96 by two non-zero natural numbers to get a square number and a cubic number. These two numbers are () and ()

Multiply 96 by two non-zero natural numbers to get a square number and a cubic number, which are (6) and (18)
96=2*2*2*3*4

(2a's Square - AB + 7) - (- 4A's square + 2Ab + 7)

(2a's Square - AB + 7) - (- 4A's square + 2Ab + 7)
=2a^2-ab+7+4a^2-2ab-7
=6a^2-3ab

As shown in the figure, in square ABCD, e is the trisection point of AD, AE = 13ad, G is the point on DC, and DG: GC = 2:7, then is be perpendicular to eg? Please state your reasons

Let's set the side length of the square ABCD as 9x, and let e be the triad point of AD, and AE = 13ad, \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's not easy +EG2 = BG2, ∧ beg is a right triangle, and ∠ beg = 90 degree, ∧ be ⊥ eg

The fourth power of 100m, the second power of n = ()
Given 4m + n = 90, 2m-3n = 10, find the quadratic power of (M + 2n) and the quadratic power of (3m-n)

The fourth power of 100m, the second power of n = (10m ^ 2n)
(M + 2n) to the power of 2 - (3m-n)
=(m+2n-3m+n)(m+2n+3m-n)
=(-2m+3n)(4m+n)
=-10×90
=-900

Sixth grade mathematics practical problems + Intelligent answers
It seems that my previous question is too simple. This time, I have a difficult one,
As like as two peas, 1, 12 table tennis balls with the same appearance and size are known as one of the inferior products. The weight of the.2,11 table tennis balls is the same. The weight of the inferior table tennis ball is different, but the.3 is slightly heavier or slightly lighter. It gives you an accurate balance and no weight.
Ask: use the balance to find out the substandard table tennis ball in three operations!
But also to determine whether the inferior table tennis is lighter or heavier than the real one!

It's not difficult. It's divided into three steps. First, put six balls on each side of the balance, which side is light, and the defective table tennis ball is over there. Second, put three balls on each side of the balance, which side is light, and the defective table tennis ball is over there. Finally, there are three balls left

A rectangle can be divided into three small squares. The perimeter of the rectangle is 24 meters. The perimeter of a small square is () and the area is ()
Answer before 3 o'clock. Be sure to be right. Answer before 15:00 on December 12, 2010,

The perimeter is (8) and the area is (4)

Calculation: (2 * 5 + 2) * (4 * 7 + 2) * (6 * 9 + 2) * *(2005*2008+2)/(1*4+2)*(3*6+2)*(5*8+2)*…… *(2004*2007+2)

The nth term of molecule = 2n (2n + 3) + 2 = 2 (n + 1) (n + 2)
Denominator n = (2n-1) (2n + 2) + 2 = 2n (2n + 1)
(2*5+2)*(4*7+2)*(6*9+2)*…… *(2005*2008+2)/(1*4+2)*(3*6+2)*(5*8+2)*…… *(2004*2007+2)
=3*4*5*6*7*8*...*2006*2007/2*3*4*5*6*7*...*2005*2006
=2007/2

It took 25 seconds for a train to pass through a 386 meter railway bridge, followed by 17 seconds for it to pass through a 236 meter long tunnel. How long is the train?

Speed
（386-236）÷（25-17）
=150÷8
=18.75 M / S
long
18.75×25-386
=468.75-386
=82.75m

The perimeter of a rectangle is 240cm, and the ratio of length to width is 3:1. How many square centimeters is the area of the rectangle
Answer in proportion

Length: width = 3:1
Length + width = 240 △ 2 = 120
So (length + width): length = (3 + 1): 3 = 4:3
That is 120: length = 4:3
Length = 120 × 3 △ 4 = 90
Width = 120-90 = 30
Area = 90 × 30 = 2700 square centimeter