Question

In a two digit number the digit at the unit place is equal to the square of the

Answer 1

Let the digit in the tens position be x, and the unit digit be y.

The number would be represented as 10x + y

10x + y + 54 = 10y + x

but y = x2

So our equation turns to,

10x + x2 + 54 = 10x2 + x

If we rearrange the equation by collecting like terms, we get a quadratic equation in the form of

9x2 - 9x - 54 = 0

Divide through by 9,

x2 - x - 6 = 0

x2 + 2x - 3x - 6 = 0

x(x + 2) - 3(x+2) = 0

(x+2) (x-3) = 0

x+2 = 0 or x-3 = 0

x = -2 or x = 3

Now x can't be negative, so x, the digit in the tens position equals 3

y = x2

y = 3^2 = 9

So our number is 39

To confirm,

39 + 54 = 93