Question

Find two consecutive positive even integers such that their product is 1520.

Answer 1

Let the first integer be x.

So, the second integer would be x + 2.

Product of the two numbers = x(x + 2)

According to the question,

⇒ x(x + 2) = 1520

⇒ x² + 2x = 1520

⇒ x² + 2x – 1520 = 0

⇒ x² + (40 – 38)x – 1520 = 0

⇒ x² + 40x – 38x – 1520 = 0

⇒ x(x + 40) – 38(x + 40) = 0

⇒ (x – 38) (x + 40) = 0

⇒ x – 38 = 0 or x + 40 = 0

⇒ x = 38 or x = – 40

Because the numbers to be discovered are positive even integers

∴ x = 38

The first number = 38

The second number = 38 + 2 = 40

Therefore, 38 and 40 are needed as the numbers.