The sum of the reciprocal of two natural numbers is 7 12, what are these two numbers?

It's 3 and 4.

That's right! Of course.

In fact, there are other solutions.

For example, 2 and 12 are also a good choice.

Ha ha! <>

These two natural numbers are 3 and 4 respectively.

The reciprocal of 3 is 1 3, the reciprocal of 4 is 1 4, and the sum of the two is 7 12, which is in line with the title.

There is more than one solution to this problem.

In addition to 3,4, there is 2,12 [1 3+1 4=7 12;1/2+1/12=7/12】

As long as you write the two simplest sets of the above two sets of fill-in-the-blank questions before junior high school, you will be done.

But in fact, it is necessary to investigate whether there is any other solution to this problem besides the simplest one....

consists of 1 n+1 m=(m+n) mn=7 12=7k 12k (k n*).

Construct x -7kx + 12k = 0

When the equation has an integer solution, the corresponding k is the solution.

It's still a bit vague here.

But considering that the root finding formula = (49k -48k).

So 49k -48k is all over as long as it's perfectly squared.

49k²-48k=t²

7k)² 2*24/7 *7k +(24/7)²-24/7)²=t²

7k - 24/7+t)(7k - 24/7-t)=(24/7)²

49k +t-24)(49k-t-24)=24²=576

Here it will be 49k-24=u

then (u+t)(u-t)=576

Obviously,The first 2 factors are integers

And u+t, u-t must be odd and even, and t cannot be 0

So we continue to weed out odd x even and 24x24

The remaining solution is a system of binary linear equations.

18x32, corresponding to u+t=32, u-t=18, corresponding to u=25, t=7, k=1, so x -7x+12=0 further know that these two numbers are 3 and 4

16x36, corresponding to u+t=36, u-t=16, corresponding to u=26, t=10, k=50 49, non-integer solution.

12x48, corresponding to u+t=48, u-t=12, corresponding to u=30, t=18, k=54 49, non-integer solution.

8x72, corresponding to u+t=72, u-t=8, corresponding to u=40, t=32, k=64 49, non-integer solution.

6x96, corresponding to u+t=96, u-t=6, corresponding to u=51, t=45, k=75 49, non-integer solution.

4x144, corresponding to u+t=144, u-t=4, corresponding to u=74, t=70, k=2, so x -14x+24=0 further know that these two numbers are 2 and 12

2x288, corresponding to u+t=288, u-t=2, corresponding to u=145, t=143, k=169 49, non-integer solution.

In summary,There are indeed only 2 sets of solutions to this problem (i.e., 3, 4 and 2, 12), and there is no other solution.

These two numbers can be: 2 and 12; Or: 3 and 4.

Analysis: 7 12=1 12+6 12=1 12+1 2;7/12=3/12+4/12=1/4+1/3。So these two numbers can be: 2 and 12; Or: 3 and 4.

Reciprocal is a mathematical term that refers to the mathematical assumption of a number x and its multiplication product of 1 number, denoted as 1 x, which means that all numbers except 0 have reciprocal numbers, the numerator and denominator are inverted and the two numbers whose product is 1 are reciprocal to each other, and 0 has no reciprocal.

Reciprocal with fractions. The fraction is turned into a false fraction, and then the numerator and denominator are reversed, which is the reciprocal of the number. In higher mathematics, complex numbers also have reciprocal numbers, such as the reciprocal of i is i.

In number theory, there is also the concept of the reciprocal of number theory, if the product of two numbers a and b, their product is about modulo m and more than 1, then we call each other the reciprocal of number theory with respect to modulo m. For example, 2*3=1 (mod5).

So 3 is 2, the number theory reciprocal about 5 The number theory reciprocal is very important in the Chinese remainder theorem. Whereas, tossing and dividing provides a method for calculating the reciprocal of number theory.

Negative reciprocal:

For example, the negative reciprocal of 1 is 1, the negative reciprocal of 1 3 is 3, the negative reciprocal of 4 5 is 5 4, and the negative reciprocal of 3 is 1 3......

1. Because zero multiplying any number does not equal 1, there is no negative reciprocal for zero.

2. Not to be confused with "reciprocal", "reciprocal" means that the product of two real numbers is 1, then these two numbers are reciprocal to each other.

3. Negative reciprocal and reciprocal both appear in pairs, and a single number cannot be called a reciprocal or negative reciprocal.

These two numbers can be: 2 and 12; Or: 3 and 4 Or 6 and 127 12=1 12+6 12=1 12+1 2 So these two numbers could be 2 and 12

7 12=3 12+4 12=1 4+1 3 So these two numbers could be 3 and 4

7 12=2 12+5 12=1 6+5 12 So these two numbers could be 6 and 12

Let these two numbers be x and y, then.

1/x+1/y=7/12

x+y)/xy=7/12

then x+y=7 xy=12

Solve x and y, one is 3, and the other is 4

So the two numbers are 3 and 4

These two numbers are 2 and 12 because the reciprocal of 2 is.

The reciprocal of 12 2 is, 12 1 12 + 1 2 = 7 12. It's not fixed.

12=3×4

So these two natural numbers are 3 and 4 respectively

7/12=1/12+6/12

So these two numbers can be: 2 and 12; Or: 3 and 4.

Actually, the solution to this problem is very simple, and now you can directly tell the answer, these two natural numbers are 3 and 4, and its reciprocal is 1/3 and 1/4, and together it is 7 12

The sum of the reciprocal of two natural numbers is 7 12

These numbers are 2,12 or 3,4, respectively

Because 1 2+1 12=1 3+1 4=7 12, there are two solutions.

The sum of the reciprocal of two natural numbers is 7 12, what are these two numbers?

So the two numbers are 3 and 4 respectively

The sum of the reciprocal of two natural numbers is 7 12, and these two numbers are 3 and 4 respectively.

7 12 = 3 12 + 4 12 = + is the reciprocal of 4 and the reciprocal of 3, and these two numbers are 4 and 3 respectively.

7 12 = 1 12 + 1 12 = 1 12+, 1 12 is the reciprocal of 12, is the reciprocal of 2, and these two numbers are 12 and 2.

To sum up, these two numbers are 3 and 4 or 2 and 12.

A: These two numbers are 2 and 12, or 3 and 4, respectively.

Because 1 3 1 4

So these two numbers are 3 and 4 respectively.

The sum of one-third and one-quarter is seven-twelve. Then these two natural numbers are three and four.

The sum of the reciprocal of two natural numbers is 7 12, how should it be calculated in this case?

The product of the reciprocal of the column equation is one, and the sum of its reciprocal is 7 12 column equations.

The sum of the reciprocal of two natural numbers is 7 12, and these two numbers are (12) and (2), or 3 and 4

The sum of the reciprocal of two natural numbers is 7 12, and these two numbers are (12) and (2), or 3 and 4

From the inscription, it can be seen that the product of these two natural numbers is 12 and sum is 7, and only the product of is 12 and and is 7, so these two natural numbers are 3 and 4;

So the answer is: 3, 4

These two natural numbers are 1 3, the reciprocal of 4 is 1 4, and the sum of the two is 7 12, which is in line with the title.

These two natural numbers end with 3 and 1 3 respectively, and 4 ends with the penultimate 1 4 and 7 12 respectively.

The reciprocal of these two natural numbers is 1 3 and 4 is 1 4, and the sum of the two is 7 12.

Did you make a mistake in that data? How is the sum of the penultimate twelve thousandths? 12 1, isn't that 12? He's an integer!

If you say that their difference is 7, then you can be 7=9-2 or 8-1.

Let these two natural numbers be x, x+7, according to the title.

1/x+1/(x+7)=1/12.

Remove the denominator to get 12(x+7+x)=x(x+7), 24x+84=x 2+7x, x 2-17x-84=0, x>0, x=21, x+7=28

Accumulation of simple slow car: 7 7 12 = 12

The product of 12: 1 12, 2 6, 3 4

Because sum = 7, 3 ten 4 = 7

So which spike is it: 3, block 4