Question

In a two digit number,the unit's digit exceeds its ten's digit by 2.The product of the given number and the sum of its digits is equal to 144.Find the number ​

Answer 1

Step-by-step explanation:

Let the tens digit be x

therefore unit digit will be x+2

therefore the number Will be 10x+x+2

the sum of the digit = 2x+2

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

(11x+2)2(x+1)=144

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

11x²+11x+2x+2=72

11x²+13x-70=0

-13+-√(169+4×770)/22

-13+-√(169+3080)/22

-13+-√(3249)/22

-13+-57/22

-13+-57/22

and continue further

Answer 2

Answer:

Answer: The required number is 24.

Step-by-step explanation:  Let (10x + y) be the number, where 'x' is the ten's digit and 'y' is the unit's digit.

According to the given information, we have

y = x + 2 -----------------(i)

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

Substituting the value of 'y' from equation (i) in equation (ii), we have

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

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

taking 2 common

2 (11x+ 2)(x + 1) = 144

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

multiplying the brackets

${11x}^2 +{11x} + { 2x} + {4} {= } 72$

${11x}^2 +{13x} + {2} {= } 72$

${11x}^2 +{13x} + {2} {= } 72$

${11x}^2 +{13x} + {70} {= } 0$

${11x}^2 +{13x} + {72} {= } 0$

${11x}^2 +{35x} {-} {22x} + {72} {= } 0$

$x {(11x + 35)} {-} 2{(11x + 35} {= } 0$

${(11x + 35)} + {( x - 2) } {= } 0$

x - 2 = 0 11x + 35 = 0

x = 2 x = -35 / 2

Since the ten's digit 'x' of the number cannot be a fraction or negative, so x = 2.

Therefore, from equation (i), we get

y = x + 2

y = 4

10x + y = 10 × 2 + 4 = 24

Thus, the required number is given by