Amenika
Amenika Amenika
  • 02-02-2020
  • Mathematics
contestada

Prove that the sum of ab and ba is divisible by the sum of a and b

Prove that the sum of ab and ba is divisible by the sum of a and b class=

Respuesta :

KerryEye KerryEye
  • 08-02-2020

Answer:

It is divisible by 11 and (a + b) !

Step-by-step explanation:

Given a two digit number [tex]$ ab $[/tex], the digits written in reverse order is [tex]$ba $[/tex].

Note that a two digit number ab  = 10a + b.

For example: 24 = 10(2) + 4

Similarly, ba = 10(b) + a

Now, the sum of the numbers ab and ba = 10a + b + 10b + a

= 11a + 11b

= 11(a + b)

Hence, the sum of any two digit number ab and the reverse of the number ba,  is divisible by 11 and (a + b).

Hence, proved.

Answer Link

Otras preguntas

Which disorder is more common in males than females, and shows up in social behaviors such as lying, theft, violence, aggression, and vandalism?
1+i is a zero of f(x)=x^4-2x^3-x^2+6x-6
Why does amy wu feel unwelcome in chinatown?
Suppose 90 out of 120 people said they like to work out and 5 out of every 18 of the people who like to work out have a gym membership. At the same rates, in a
is powdered drink and water a mixture or a solution
What is the theme or underlying message of mallam sile?
How was the telephone different from the telegraph?
_____ are the building blocks of protein. Carbohydrates Lipids Amino acids Nucleic acids
How did constantinople's church of hagia sophia (ayasofya) demonstrate how the byzantine empire blended with the old roman empire?
How do some human white blood cells help destroy pathogenic bacteria?