The product of 3 consecutive even numbers is equal to 20 times their sum. Find the numbers. 

Dear Student!

Let three consecutive even numbers be x – 2, x and x + 2.

Given, Product of three consecutive even numbers = 20 × (Sum of the three Consecutive number)

∴ (x – 2) × x × (x + 2) = 20 [ (x – 2) + x + (x + 2) ]

⇒ x (x² – 4) = 20 × 3x

⇒ x³ – 4x = 60 x

⇒ x³ – 64x = 0

⇒ x (x² – 64) = 0

⇒ x = 0 or x² – 64 = 0

⇒ x = 0 or x² = 64 

⇒ x = 0 or x = ± 8

When x = 0, then x – 2 = 0 – 2 = – 2 and x + 2 = 0 + 2 = 2

∴ Three consecutive even numbers are –2, 0 and 2.

When x = 8, then x – 2 = 8 – 2 = 6 and x + 2 = 8 + 2 = 10

∴ Three consecutive even numbers are 6, 8 and 10.

When x = – 8, then x – 2 = – 8 – 2 = – 10 and x + 2 = – 8 + 2 = – 6

∴ Three consecutive even numbers are – 10, – 8  and – 6.

Cheers!