Question

The difference between two numbers is 2 and their product is 1443. Find the numbers.

Answer 1

Let x be one of the numbers.

Thus, second number will be x + 2.

According to the question,

(x)(x + 2) = 1443

⇒ x² + 2x = 1443

⇒ x² + 2x – 1443 = 0

⇒ x² + (39 – 37)x – 1443 = 0

⇒ x² + 39x – 37x – 1443 = 0

⇒ x(x + 39) – 37(x + 39) = 0

⇒ (x – 37)(x + 39) = 0

⇒ (x – 37) = 0 or (x + 39) = 0

⇒ x = 37 or x = – 39

If x = 37,

Then, x + 2 = 37 + 2 = 39

Thus, the numbers 37 and 39 are two.

If x = – 39

Then, x + 2 = – 39 + 2 = – 37

So, two numbers are – 39, – 37 

Hence, the numbers are 37, 39 or – 39, – 37.