Question

Two numbers differ by 3 and their product is 504. Find the numbers.

Answer 1

Let the two numbers be x and x - 3 given that x(x + 3) = 504

⇒ x² + 3x - 504 = 0

⇒ x² + 24x - 21x - 504 = 0

⇒ x(x + 24) - 21(x + 24) = 0

⇒ (x + 24)(x - 21) = 0

Therefore,

⇒ x + 24 = 0

⇒ x = -24

Or

⇒ x - 21 = 0

⇒ x = 21

Since, x being a number,

Therefore,

When x = -24 then

x + 3 = -24 + 3 = -21

And when x = 21 then

x + 3 = 21 + 3 = 24

Thus, two consecutive numbers be either 21, 24 or -21, -24.