Question

Take a two-digit number. Write it backwards. Add it to the original number. If what you get is a perfect square, what could be the original number? Find all answers.

Answer 1

Answer: 29, 38, 47, 56, 65, 74, 83, 92

Step-by-step explanation:

Let the two digit number be xy.

The tens value is x while the unit value is y

The number is then 10x+y

If it is written backwards, it is 10y+x

(10x+y) + (10y+x)

= 10x+y+10y+x

Collect like terms

10x+x+y+10y

= 11x+11y

= 11(x+y)

For 11(x+y) to be a perfect square, (x+y) must be equal to 11. So that we have

11*11=121

The combinations of x and y to give 11 when added, is from [1,2,3,4,5,6,7,8,9]

The possible combinations yield 29, 38, 47, 56, 65,74, 83 and 92