The product of two consecutive natural numbers

Algebra (10)

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

Answer

Assume that two consecutive natural numbers which are multiples of 3 are 𝑥 𝑎𝑛𝑑 𝑥 + 3

𝑥(𝑥 + 3) = 810

𝑥2 + 3𝑥 = 810

𝑥2 + 3𝑥 - 810 = 0

(𝑥 + 30)(𝑥 - 27) = 0

𝑥 = -30 𝑜𝑟  𝑥 = 27

Therefore, the two numbers are 27 and 30.

  • Exam Year: 2019