The product of two positive integers is nine times the sum of two numbers, how many possibilities ar

Let the two numbers be a and b

then ab=9(a+b), i.e., ab-9a-9b=0, i.e.: (a-9)(b-9)=81 (Do you understand this step?) The 81 factoring factor is:

81 = 1 * 81 = 3 * 27 = 9 * 91 * 81 corresponds to the following four situations: a-9 = 1, b-9 = 81;a-9=-1，b-9=-81；a-9=81，b-9=1；a-9=-81，b-9=-1。Among them, the negative number of the key area, that is, there are 2 possibilities left.

There are also 2 possibilities for 3*27.

9*9 corresponds to the following situations: a-9=9, b-9=9;a-9=-9，b-9=-9。Stripped of the negative value, there is only one possibility left.

So there are a total of 2+2+1=5 possibilities.

Suppose the two numbers are a and b

Then there is: ab=9a+9b

There is b = 9 + 9 b a

a=9+9a/b

Suppose a>b and b a is p q after being minimalized

Then 9b a=9p q is an integer, so q is 3 or 9, and because 9a b=9q p, then p is also 3 or 9, which contradicts p q at its simplest, so p=1

So there is ab=9(a+b)=81(2+b, a + ab) which is an integer.

If q=3, then ab=81*5+81*(1 3)=432 and a=3b, so a=36, b=12, a+b=48

If q=9, then ab=81*11+81*(1 9)=900 and a=9b, so a=90, b=10, a+b=100

Two scenarios.

Let the two numbers be, respectively, by the title:

x+y-x = 4 9 --y = 4 9x+y-y = 2 9 --x = 2 9x+y = 2 9+4 9 = 6 9 = 2 3 Answer: The sum of these two numbers is 2 3

Or another way:

Let the two numbers return to know respectively, by the title:

x+y-x = 4/9

x+y-y = 2/9

The two finchs are implicitly added:

x+y-x)+(x+y-y) =4/9+2/9x+y = 6/9 = 2/3

Answer: The sum of these two numbers is 2 3

Smaller number: 9 2)=3 2=3 2 2;Larger number: (3 2 2) 2=3 2.

Or, the smaller number: -3 2;

Larger numbers: -3 2 2.

What grade? Which old.

Root number learned? <>

If you are slow to read the map, look at the group sleepy.

Solution: Let these two positive integers be x,y,respectively,then x+y>0.

x+y=10(1/x+1/y)

x+y=10(x+y)/(xy)

10/(xy)=1

The product of the two numbers xy=10 is 10.

The Handsome Wolf Hunting team will answer for you:

x+y=10(1/x+1/y)

x+y=10(x+y)/xy

xy=10, i.e. the product of these two numbers is 10.

xy=8(x+y) (x+y)=1 8xyWhen x=24, y=12, 1 8xy=1 8 24 12=36

x+y=24+12=36, the two positive integers are 24 and 12.

The volume has increased to 81 times.

Let the original two numbers be a and b

then the original product is a b

The current product is: 9a 9b = 9 9 a b = 81a b