Question

The product of two consecutive even natural numbers is 440. Find the numbers.

Answer 1

Given:

The product of two consecutive even natural numbers is 440.

Let the smaller even number be x

Then the next consecutive even number is x + 2

So, their product is:

x(x + 2) = 440

x² + 2x = 440

x² + 2x − 440 = 0

Look for two numbers whose product is −440 and sum is +2.

22 × −20 = −440 and 22 + (−20) = 2

x² + 2x − 440 = (x + 22) (x − 20) = 0

x + 22 = 0

⇒ x = −22

x − 20 = 0

⇒ x = 20

x = 20, x + 2 = 22

20 and 22​

These are the two consecutive even natural numbers whose product is 440.