Question 269964
A two-digit number. The first digit added to or multiplied by itself, or squared = the second digit. What is the number?

Let x be the tens digit and y the ones digit.

The number then is 10*x + 1*y

We are given that:

1.) 2x = y and
2.) x^2 = y

From above we have x^2 = x so

x^2 - x = 0
x*(x-1) = 0

Either x = 0 or x = 1.

If x = 0 then y = 2*0 = 0 also. In this case the number then is 10*0 + 1*0 = 0

If x = 1 then y = 2*1 = 2. In this case the number then is 10*1 + 1*2 = 12