Question

In a two digit no. ,the digit at units place is equal to the square of digit at tens place.if 54 is added to the no. The digit gets interchanged,find the no.
Plz guys give the ans. Fast its urgent

Answer 1

I bet it's 39, but let's solve it

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

They switched positions. The two things we have discovered are:

Our digit is 39

I am good at guessing

Answer 2

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

They switched positions. The things we have discovered are:

Our digit is 39

I hope it helps you !!
please mark my answer as a brainalist please please