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