Question

In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

Answer 1

Let the 2 digit number be xy, where x is tens place and y is units place digit. The value of the number will be ( 10x +y) {eg 13 = 10× 1+ 3}

According to question,

y = x+2 and
(10x+y)(x + y)= 144
just substitute y = x+2 in this equation
(10x+x+2)(x + x+2)= 144
(11x+2) (2x + 2)= 144
(11x+2) (x + 1)= 72
11x²+13x +2 =72
11x²+13x -70=0
putting x =2 will solve this equation,
you can find out the other factor of this, by dividing it by (x-2) and check for the other​ value of x.
Now, we got one value of x as 2.
y= x+2 = 4
Hence, one such number is 24. you can check whether another such number exists or not by finding the other factor and examining the zero of the quadratic. if the value comes out to be negative, it will mean that there is only one solution, which we have already found.

Answer 2

Answer:

Explanation:

y = x+2 and

(10x+y)(x + y)= 144

just substitute y = x+2 in this equation

(10x+x+2)(x + x+2)= 144

(11x+2) (2x + 2)= 144

(11x+2) (x + 1)= 72

11x²+13x +2 =72

11x²+13x -70=0

putting x =2 will solve this equation,

you can find out the other factor of this, by dividing it by (x-2) and check for the other​ value of x.

Now, we got one value of x as 2.

y= x+2 = 4

Hence, one such number is 24.