Question

Question :- 11

A two digit number contains the smaller of two digits in the unit place. The product of the digits is 40 and the difference between the digits is 3. Find the number​

Answer 1

Let the digits be x and y;

$x - y = 3 \\ x = 3 + y \\ xy = 40 \\ \\ (3 + y)(y) = 40 \\ 3y + {y}^{2} - 40 = 0 \\ {y}^{2} + 3y - 40 \\ {y}^{2} + 8y - 5y - 40 = 0 \\ y(y + 8) - 5(y + 8) \\ y = 5 \\ y = - 8 \\ \\ x = 3 + y \\ x = 8$

number is 85

Answer 2

let two numbers x and y

product of these numbers

xy=40 - -1)

difference

x-y= 3

x=3+y----2)

put value of x in 1)

(3+y)y=40

3y+y2 -40=0

y2+3y -40=0

y2+ 8y -5y-40 =0

y(y+8) -5(y+8)=0

(y-5)( y+8)=0

y=5 , -8

put in 2)

x=3+5

x=8

x=8 , Y=5

answer is 85

hope it helps