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
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