Question

two integers differ by 3 and their product is 504 find the integers​

Answer 1

Let the two natural numbers be x and y.

Given that difference of numbers are 3.

x−y=3

x=3+y⟶(1)

Also given that product of numbers is 504.

xy=504

From eq  

n

(1), we have

⇒ (3+y)y=504

⇒3y+y  

2

=504

⇒y  

2

+3y−504=0

⇒(y+24)(y−21)=0

⇒y=21 or −24

Case I:-

y=21

Substituting the value of y in eq  

n

(1), we have

x=3+y=3+21=24

Hence, x=24.

Case II:-

y=−24

Substituting the value of y in eq  

n

(1), we have

x=3+y=3+(−24)=−21

Hence, x=−21.

Hence, the numbers can be (21 and 24) or (-21 and -24).