The sum of the digits of a two digit number is 12. The tens digit is the square of it's units digit. Find the number

Answer 1

Let the number be a and b.

a + b = 12

The tens digit is the square of it's units digit means:

a = b²

So:

a + b = 12

Replace a by b² in this equation.

b² + b = 12

Subtract 12 to both sides.

b² + b - 12 = 0

Try to solve this quadratic equation.

The solutions are:

b = - 4 and b = 3

For b = - 4

a = b² = ( - 4 )² = 16

You have to reject this solution because a and b are single-digit numbers and 16 is a two-digit number.

For b = 3

a = b² = 3² = 9

The solution is:

a = 9 , b = 3

The number is 93.

Check result.

a = b²

9 = 3²

a + b = 9 + 3 = 12